Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion.
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79 items
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Updated
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2
fact
stringlengths 5
16.9k
| type
stringclasses 3
values | library
stringclasses 1
value | imports
listlengths 1
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| filename
stringclasses 545
values | symbolic_name
stringlengths 1
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stringclasses 1
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|---|---|---|---|---|---|---|
Formula : Type where const : ℕ → Formula _∧_ : Formula → Formula → Formula _∨_ : Formula → Formula → Formula ¬_ : Formula → Formula ⊥ : Formula ⊤ : Formula
|
data
|
Cubical
|
[
"open import Cubical.HITs.SetQuotients.Base",
"open import Cubical.HITs.SetQuotients.Properties",
"open import Cubical.Foundations.Prelude hiding (_∧_; _∨_)",
"open import Cubical.Relation.Binary.Base",
"open import Cubical.Data.Nat.Base",
"open import Cubical.Data.Prod.Base",
"open import Cubical.Algebra.DistLattice.Base"
] |
Cubical/Algebra/LindenbaumTarski.agda
|
Formula
| |
ctxt : Type where ∅ : ctxt _∷_ : ctxt → Formula → ctxt
|
data
|
Cubical
|
[
"open import Cubical.HITs.SetQuotients.Base",
"open import Cubical.HITs.SetQuotients.Properties",
"open import Cubical.Foundations.Prelude hiding (_∧_; _∨_)",
"open import Cubical.Relation.Binary.Base",
"open import Cubical.Data.Nat.Base",
"open import Cubical.Data.Prod.Base",
"open import Cubical.Algebra.DistLattice.Base"
] |
Cubical/Algebra/LindenbaumTarski.agda
|
ctxt
| |
_ ∈_ : Formula → ctxt → Type where Z : ∀ {Γ ϕ} → ϕ ∈ Γ ∷ ϕ S : ∀ {Γ ϕ ψ} → ϕ ∈ Γ → ϕ ∈ Γ ∷ ψ -- Provability
|
data
|
Cubical
|
[
"open import Cubical.HITs.SetQuotients.Base",
"open import Cubical.HITs.SetQuotients.Properties",
"open import Cubical.Foundations.Prelude hiding (_∧_; _∨_)",
"open import Cubical.Relation.Binary.Base",
"open import Cubical.Data.Nat.Base",
"open import Cubical.Data.Prod.Base",
"open import Cubical.Algebra.DistLattice.Base"
] |
Cubical/Algebra/LindenbaumTarski.agda
|
_
| |
_ ⊢_ : ctxt → Formula → Type where ∧-I : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ϕ → Γ ⊢ ψ → Γ ⊢ ϕ ∧ ψ ∧-E₁ : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ϕ ∧ ψ → Γ ⊢ ϕ ∧-E₂ : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ϕ ∧ ψ → Γ ⊢ ψ ∨-I₁ : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ψ → Γ ⊢ ϕ ∨ ψ ∨-I₂ : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ϕ → Γ ⊢ ϕ ∨ ψ ∨-E : {Γ : ctxt} {ϕ ψ γ : Formula} → Γ ⊢ ϕ ∨ ψ → Γ ∷ ϕ ⊢ γ → Γ ∷ ψ ⊢ γ → Γ ⊢ γ ¬-I : {Γ : ctxt} {ϕ : Formula} → Γ ∷ ϕ ⊢ ⊥ → Γ ⊢ ¬ ϕ ¬-E : {Γ : ctxt} {ϕ : Formula} → Γ ⊢ ϕ → Γ ⊢ ¬ ϕ → Γ ⊢ ⊥ ⊥-E : {Γ : ctxt} {ϕ : Formula} → Γ ⊢ ⊥ → Γ ⊢ ϕ ⊤-I : {Γ : ctxt} → Γ ⊢ ⊤ axiom : {Γ : ctxt} {ϕ : Formula} → ϕ ∈ Γ → Γ ⊢ ϕ LEM : {Γ : ctxt} {ϕ : Formula} → Γ ⊢ ¬ ϕ ∨ ϕ weakening : {Γ : ctxt} {ϕ ψ : Formula} → Γ ⊢ ψ → Γ ∷ ϕ ⊢ ψ
|
data
|
Cubical
|
[
"open import Cubical.HITs.SetQuotients.Base",
"open import Cubical.HITs.SetQuotients.Properties",
"open import Cubical.Foundations.Prelude hiding (_∧_; _∨_)",
"open import Cubical.Relation.Binary.Base",
"open import Cubical.Data.Nat.Base",
"open import Cubical.Data.Prod.Base",
"open import Cubical.Algebra.DistLattice.Base"
] |
Cubical/Algebra/LindenbaumTarski.agda
|
_
| |
FinMatrix : (A : Type ℓ) (m n : ℕ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Structure",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Functions.FunExtEquiv",
"import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Nat renaming ( _+_ to _+ℕ_ ; _·_ to _·ℕ_",
"open import Cubical.Data.Vec",
"open import Cubical.Data.Sigma.Base",
"open import Cubical.Data.FinData",
"open import Cubical.Relation.Nullary",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Monoid",
"open import Cubical.Algebra.Ring",
"open import Cubical.Algebra.Ring.BigOps",
"open import Cubical.Algebra.CommRing"
] |
Cubical/Algebra/Matrix.agda
|
FinMatrix
| |
VecMatrix : (A : Type ℓ) (m n : ℕ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Structure",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Functions.FunExtEquiv",
"import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Nat renaming ( _+_ to _+ℕ_ ; _·_ to _·ℕ_",
"open import Cubical.Data.Vec",
"open import Cubical.Data.Sigma.Base",
"open import Cubical.Data.FinData",
"open import Cubical.Relation.Nullary",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Monoid",
"open import Cubical.Algebra.Ring",
"open import Cubical.Algebra.Ring.BigOps",
"open import Cubical.Algebra.CommRing"
] |
Cubical/Algebra/Matrix.agda
|
VecMatrix
| |
FinMatrixIsoVecMatrix : (A : Type ℓ) (m n : ℕ) → Iso (FinMatrix A m n) (VecMatrix A m n)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Structure",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Functions.FunExtEquiv",
"import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Nat renaming ( _+_ to _+ℕ_ ; _·_ to _·ℕ_",
"open import Cubical.Data.Vec",
"open import Cubical.Data.Sigma.Base",
"open import Cubical.Data.FinData",
"open import Cubical.Relation.Nullary",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Monoid",
"open import Cubical.Algebra.Ring",
"open import Cubical.Algebra.Ring.BigOps",
"open import Cubical.Algebra.CommRing"
] |
Cubical/Algebra/Matrix.agda
|
FinMatrixIsoVecMatrix
| |
flatten : {n m : ℕ} → FinMatrix A n m → FinVec A (n ·ℕ m)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Structure",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Functions.FunExtEquiv",
"import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Nat renaming ( _+_ to _+ℕ_ ; _·_ to _·ℕ_",
"open import Cubical.Data.Vec",
"open import Cubical.Data.Sigma.Base",
"open import Cubical.Data.FinData",
"open import Cubical.Relation.Nullary",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Monoid",
"open import Cubical.Algebra.Ring",
"open import Cubical.Algebra.Ring.BigOps",
"open import Cubical.Algebra.CommRing"
] |
Cubical/Algebra/Matrix.agda
|
flatten
| |
SymGroup : (X : Type ℓ) → isSet X → Group ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Structure",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Nat",
"open import Cubical.Data.SumFin",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Unit",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.GroupPath",
"open import Cubical.Algebra.Group.Instances.Bool",
"open import Cubical.Algebra.Group.Instances.Unit"
] |
Cubical/Algebra/SymmetricGroup.agda
|
SymGroup
| |
FinSymGroup : ℕ → Group₀
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Structure",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Nat",
"open import Cubical.Data.SumFin",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Unit",
"open import Cubical.Algebra.Group",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.GroupPath",
"open import Cubical.Algebra.Group.Instances.Bool",
"open import Cubical.Algebra.Group.Instances.Unit"
] |
Cubical/Algebra/SymmetricGroup.agda
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FinSymGroup
| |
satAC : (ℓ' : Level) (n : ℕ) (A : Type ℓ) → Type (ℓ-max ℓ (ℓ-suc ℓ'))
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Fin",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.PropositionalTruncation as PT"
] |
Cubical/Axiom/Choice.agda
|
satAC
| |
satAC₀ : {A : Type ℓ} → satAC ℓ' 0 A
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Fin",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.PropositionalTruncation as PT"
] |
Cubical/Axiom/Choice.agda
|
satAC₀
| |
FinSatAC : (n m : ℕ) → ∀ {ℓ} → satAC ℓ n (Fin m)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Fin",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.PropositionalTruncation as PT"
] |
Cubical/Axiom/Choice.agda
|
FinSatAC
| |
InductiveFinSatAC : (n m : ℕ) → ∀ {ℓ} → satAC ℓ n (Fin m)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Fin",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.PropositionalTruncation as PT"
] |
Cubical/Axiom/Choice.agda
|
InductiveFinSatAC
| |
LLPO : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
LLPO
| |
isPropLLPO : isProp (LLPO A)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
isPropLLPO
| |
WLPO : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
WLPO
| |
WLPO' : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
WLPO'
| |
isPropWLPO : isProp (WLPO A)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
isPropWLPO
| |
isPropWLPO' : isProp (WLPO' A)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
isPropWLPO'
| |
LPO : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Empty as Empty",
"open import Cubical.Data.Sum as Sum",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Axiom/Omniscience.agda
|
LPO
| |
Path : ∀ {ℓ} (A : Type ℓ) → A → A → Type ℓ
|
function
|
Cubical
|
[
"open import Agda.Builtin.Cubical.Path public",
"open import Agda.Builtin.Cubical.Sub public",
"open import Agda.Primitive.Cubical public",
"import Agda.Builtin.Cubical.Glue",
"open import Agda.Primitive public",
"open import Agda.Builtin.Sigma public"
] |
Cubical/Core/Primitives.agda
|
Path
| |
Σ-syntax : ∀ {ℓ ℓ'} (A : Type ℓ) (B : A → Type ℓ') → Type (ℓ-max ℓ ℓ')
|
function
|
Cubical
|
[
"open import Agda.Builtin.Cubical.Path public",
"open import Agda.Builtin.Cubical.Sub public",
"open import Agda.Primitive.Cubical public",
"import Agda.Builtin.Cubical.Glue",
"open import Agda.Primitive public",
"open import Agda.Builtin.Sigma public"
] |
Cubical/Core/Primitives.agda
|
Σ-syntax
| |
yieldsCWskel : (ℕ → Type ℓ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
yieldsCWskel
| |
CWskel : (ℓ : Level) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
CWskel
| |
yieldsFinCWskel : (n : ℕ) (X : ℕ → Type ℓ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
yieldsFinCWskel
| |
finCWskel : (ℓ : Level) → (n : ℕ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
finCWskel
| |
isFinCWskel : ∀ {ℓ} (C : CWskel ℓ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
isFinCWskel
| |
realiseSeq : CWskel ℓ → Sequence ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
realiseSeq
| |
realiseFinSeq : (m : ℕ) → CWskel ℓ → FinSequence m ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
realiseFinSeq
| |
realise : CWskel ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
realise
| |
hasCWskel : (X : Type ℓ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
hasCWskel
| |
isCW : (X : Type ℓ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
isCW
| |
CW : (ℓ : Level) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
CW
| |
CWexplicit : (ℓ : Level) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
CWexplicit
| |
isFinIsCW : {X : Type ℓ} → hasCWskel X → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
isFinIsCW
| |
hasFinCWskel : (X : Type ℓ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
hasFinCWskel
| |
isFinCW : (X : Type ℓ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
isFinCW
| |
finCW : (ℓ : Level) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
finCW
| |
finCWexplicit : (ℓ : Level) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
finCWexplicit
| |
cofibCW : ∀ {ℓ} (n : ℕ) (C : CWskel ℓ) → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
cofibCW
| |
to_cofibCW : (n : ℕ) (C : CWskel ℓ) → fst C (suc n) → cofibCW n C
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
to_cofibCW
| |
δ : (n : ℕ) (C : CWskel ℓ) → cofibCW n C → Susp (fst C n)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Base.agda
|
δ
| |
yieldsConnectedCWskel : (A : ℕ → Type ℓ) (n : ℕ) → Type _
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
yieldsConnectedCWskel
| |
yieldsCombinatorialConnectedCWskel : (A : ℕ → Type ℓ) (n : ℕ) → Type _
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
yieldsCombinatorialConnectedCWskel
| |
connectedCWskel : (ℓ : Level) (n : ℕ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
connectedCWskel
| |
combinatorialConnectedCWskel : (ℓ : Level) (n : ℕ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
combinatorialConnectedCWskel
| |
isConnectedCW : ∀ {ℓ} (n : ℕ) → Type ℓ → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
isConnectedCW
| |
isConnectedCW' : ∀ {ℓ} (n : ℕ) → Type ℓ → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
isConnectedCW'
| |
ConnectedCW : (ℓ : Level) (n : ℕ) → Type (ℓ-suc ℓ)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Instances.SphereBouquetMap",
"open import Cubical.CW.Subcomplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Sum as ⊎",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Bool",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT hiding (elimFin)",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.HITs.Wedge",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected",
"open import Cubical.Homotopy.Group.Base",
"open import Cubical.Homotopy.Group.Properties",
"open import Cubical.Homotopy.Group.PiCofibFinSphereBouquetMap",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup.Base",
"open import Cubical.Algebra.AbGroup.FinitePresentation",
"open import Cubical.CW.Instances.Lift"
] |
Cubical/CW/Connected.agda
|
ConnectedCW
| |
cellHom {C : CWskel ℓ} {D : CWskel ℓ'} (f g : cellMap C D) : Type (ℓ-max ℓ ℓ') where constructor cellhom open SequenceMap field hom : (n : ℕ) → (x : C .fst n) → CW↪ D n (f .map n x) ≡ CW↪ D n (g .map n x) coh : (n : ℕ) → (c : C .fst n) → Square (cong (CW↪ D (suc n)) (hom n c)) (hom (suc n) (CW↪ C n c)) (cong (CW↪ D (suc n)) (f .comm n c)) (cong (CW↪ D (suc n)) (g .comm n c)) -- Finite cellular homotopies
|
record
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.CW.ChainComplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SetTruncation as ST hiding (map)",
"open import Cubical.HITs.Truncation as TR hiding (map)",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.ZCohomology.Base",
"open import Cubical.ZCohomology.Properties",
"open import Cubical.ZCohomology.GroupStructure",
"open import Cubical.ZCohomology.Groups.Sn"
] |
Cubical/CW/Homotopy.agda
|
cellHom
| |
finCellHom (m : ℕ) {C : CWskel ℓ} {D : CWskel ℓ'} (f g : finCellMap m C D) : Type (ℓ-max ℓ ℓ') where constructor fincellhom open FinSequenceMap field fhom : (n : Fin (suc m)) (x : C .fst (fst n)) → CW↪ D (fst n) (f .fmap n x) ≡ CW↪ D (fst n) (g .fmap n x) fcoh : (n : Fin m) (c : C .fst (fst n)) → Square (cong (CW↪ D (suc (fst n))) (fhom (injectSuc n) c)) (fhom (fsuc n) (CW↪ C (fst n) c)) (cong (CW↪ D (suc (fst n))) (f .fcomm n c)) (cong (CW↪ D (suc (fst n))) (g .fcomm n c))
|
record
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.CW.ChainComplex",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SetTruncation as ST hiding (map)",
"open import Cubical.HITs.Truncation as TR hiding (map)",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.ZCohomology.Base",
"open import Cubical.ZCohomology.Properties",
"open import Cubical.ZCohomology.GroupStructure",
"open import Cubical.ZCohomology.Groups.Sn"
] |
Cubical/CW/Homotopy.agda
|
finCellHom
| |
cellMap : (C : CWskel ℓ) (D : CWskel ℓ') → Type (ℓ-max ℓ ℓ')
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.ChainComplex",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Map.agda
|
cellMap
| |
realiseCellMap : cellMap C D → realise C → realise D
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.ChainComplex",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Map.agda
|
realiseCellMap
| |
idCellMap : (C : CWskel ℓ) → cellMap C C
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.ChainComplex",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Map.agda
|
idCellMap
| |
composeCellMap : (g : cellMap D E) (f : cellMap C D) → cellMap C E
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.GroupoidLaws",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Int renaming (_·_ to _·ℤ_ ; -_ to -ℤ_)",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.ChainComplex",
"open import Cubical.HITs.S1",
"open import Cubical.HITs.Sn.Degree",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.SphereBouquet.Degree",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.Algebra.Group.MorphismProperties",
"open import Cubical.Algebra.Group.Morphisms",
"open import Cubical.Algebra.ChainComplex",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Map.agda
|
composeCellMap
| |
CW₀-empty : (C : CWskel ℓ) → ¬ fst C 0
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv.Properties",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected"
] |
Cubical/CW/Properties.agda
|
CW₀-empty
| |
CW₁-discrete : (C : CWskel ℓ) → fst C 1 ≃ Fin (snd C .fst 0)
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv.Properties",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected"
] |
Cubical/CW/Properties.agda
|
CW₁-discrete
| |
isSet-CW₀ : (C : CWskel ℓ) → isSet (fst C (suc zero))
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv.Properties",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected"
] |
Cubical/CW/Properties.agda
|
isSet-CW₀
| |
realiseFin : (n : ℕ) (C : finCWskel ℓ n) → Iso (fst C n) (realise (finCWskel→CWskel n C))
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv.Properties",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected"
] |
Cubical/CW/Properties.agda
|
realiseFin
| |
satAC-CW₁ : (n : ℕ) (C : CWskel ℓ) → satAC ℓ' n (fst C (suc zero))
|
function
|
Cubical
|
[
"open import Cubical.CW.Base",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Pointed",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv.Properties",
"open import Cubical.Data.Nat renaming (_+_ to _+ℕ_)",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Sequence",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.Susp",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.SphereBouquet",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.Truncation as TR",
"open import Cubical.Algebra.AbGroup",
"open import Cubical.Algebra.AbGroup.Instances.FreeAbGroup",
"open import Cubical.Axiom.Choice",
"open import Cubical.Relation.Nullary",
"open import Cubical.Homotopy.Connected"
] |
Cubical/CW/Properties.agda
|
satAC-CW₁
| |
subCWExplicit : ∀ {ℓ} (n : ℕ) → CWexplicit ℓ → CWexplicit ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Subcomplex.agda
|
subCWExplicit
| |
subCW : ∀ {ℓ} (n : ℕ) → CWexplicit ℓ → CW ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Subcomplex.agda
|
subCW
| |
niceFinCWskel : ∀ {ℓ} (n : ℕ) → finCWskel ℓ n → finCWskel ℓ n
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Subcomplex.agda
|
niceFinCWskel
| |
makeNiceFinCWskel : ∀ {ℓ} {A : Type ℓ} → hasFinCWskel A → hasFinCWskel A
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Subcomplex.agda
|
makeNiceFinCWskel
| |
makeNiceFinCW : ∀ {ℓ} → finCW ℓ → finCW ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Fin.Base",
"open import Cubical.Data.Fin.Properties",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Empty as ⊥",
"open import Cubical.Data.Nat.Order.Inductive",
"open import Cubical.Data.Sequence",
"open import Cubical.Data.FinSequence",
"open import Cubical.CW.Base",
"open import Cubical.CW.Properties",
"open import Cubical.CW.Map",
"open import Cubical.HITs.SequentialColimit",
"open import Cubical.HITs.Sn",
"open import Cubical.HITs.Pushout",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/CW/Subcomplex.agda
|
makeNiceFinCW
| |
isFinInd : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Data.Nat",
"open import Cubical.Data.SumFin",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Functions.Surjection",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.S1"
] |
Cubical/Data/FinInd.agda
|
isFinInd
| |
isFinInd-S¹ : isFinInd S¹
|
function
|
Cubical
|
[
"open import Cubical.Data.Nat",
"open import Cubical.Data.SumFin",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Functions.Surjection",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.HITs.S1"
] |
Cubical/Data/FinInd.agda
|
isFinInd-S¹
| |
isSubFinSet : Type ℓ → Type ℓ
|
function
|
Cubical
|
[
"open import Cubical.Data.Nat",
"open import Cubical.Data.SumFin",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Functions.Embedding",
"open import Cubical.HITs.PropositionalTruncation as PT",
"open import Cubical.Relation.Nullary"
] |
Cubical/Data/SubFinSet.agda
|
isSubFinSet
| |
UARel (A : Type ℓA) (ℓ≅A : Level) : Type (ℓ-max ℓA (ℓ-suc ℓ≅A)) where no-eta-equality constructor uarel field _≅_ : A → A → Type ℓ≅A ua : (a a' : A) → (a ≅ a') ≃ (a ≡ a') uaIso : (a a' : A) → Iso (a ≅ a') (a ≡ a') uaIso a a' = equivToIso (ua a a') ≅→≡ : {a a' : A} (p : a ≅ a') → a ≡ a' ≅→≡ {a} {a'} = Iso.fun (uaIso a a') ≡→≅ : {a a' : A} (p : a ≡ a') → a ≅ a' ≡→≅ {a} {a'} = Iso.inv (uaIso a a') ρ : (a : A) → a ≅ a ρ a = ≡→≅ refl
|
record
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Sigma",
"open import Cubical.Relation.Binary"
] |
Cubical/Displayed/Base.agda
|
UARel
| |
DUARel {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) (B : A → Type ℓB) (ℓ≅B : Level) : Type (ℓ-max (ℓ-max ℓA ℓB) (ℓ-max ℓ≅A (ℓ-suc ℓ≅B))) where no-eta-equality constructor duarel open UARel 𝒮-A field _≅ᴰ⟨_⟩_ : {a a' : A} → B a → a ≅ a' → B a' → Type ℓ≅B uaᴰ : {a a' : A} (b : B a) (p : a ≅ a') (b' : B a') → (b ≅ᴰ⟨ p ⟩ b') ≃ PathP (λ i → B (≅→≡ p i)) b b' fiberRel : (a : A) → Rel (B a) (B a) ℓ≅B fiberRel a = _≅ᴰ⟨ ρ a ⟩_ uaᴰρ : {a : A} (b b' : B a) → b ≅ᴰ⟨ ρ a ⟩ b' ≃ (b ≡ b') uaᴰρ {a} b b' = compEquiv (uaᴰ b (ρ _) b') (substEquiv (λ q → PathP (λ i → B (q i)) b b') (secEq (ua a a) refl)) ρᴰ : {a : A} → (b : B a) → b ≅ᴰ⟨ ρ a ⟩ b ρᴰ {a} b = invEq (uaᴰρ b b) refl -- total UARel induced by a DUARel
|
record
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Transport",
"open import Cubical.Data.Sigma",
"open import Cubical.Relation.Binary"
] |
Cubical/Displayed/Base.agda
|
DUARel
| |
𝒮-generic : (A : Type ℓA) → UARel A ℓA
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Transport",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Generic.agda
|
𝒮-generic
| |
𝒮ᴰ-generic : {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) (B : A → Type ℓB) → DUARel 𝒮-A B ℓB
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Transport",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Generic.agda
|
𝒮ᴰ-generic
| |
𝒮ˢ-generic : {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) (B : A → Type ℓB) → SubstRel 𝒮-A B
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Transport",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Generic.agda
|
𝒮ˢ-generic
| |
UARelHom {A : Type ℓA} {B : Type ℓB} (𝒮-A : UARel A ℓ≅A) (𝒮-B : UARel B ℓ≅B) : Type (ℓ-max (ℓ-max ℓA ℓ≅A) (ℓ-max ℓB ℓ≅B)) where no-eta-equality constructor uarelhom field fun : A → B rel : ∀ {a a'} → UARel._≅_ 𝒮-A a a' → UARel._≅_ 𝒮-B (fun a) (fun a') ua : ∀ {a a'} (p : UARel._≅_ 𝒮-A a a') → cong fun (UARel.≅→≡ 𝒮-A p) ≡ UARel.≅→≡ 𝒮-B (rel p)
|
record
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Transport",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Morphism.agda
|
UARelHom
| |
𝒮-id : {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) → UARelHom 𝒮-A 𝒮-A
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Transport",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Morphism.agda
|
𝒮-id
| |
𝒮-prop : (P : hProp ℓP) → UARel (P .fst) ℓ-zero
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Unit",
"open import Cubical.Displayed.Base"
] |
Cubical/Displayed/Prop.agda
|
𝒮-prop
| |
DUAFields {ℓA ℓ≅A ℓR ℓ≅R} {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) (R : A → Type ℓR) (_≅R⟨_⟩_ : {a a' : A} → R a → UARel._≅_ 𝒮-A a a' → R a' → Type ℓ≅R) : ∀ {ℓS ℓ≅S} {S : A → Type ℓS} (πS : ∀ {a} → R a → S a) (𝒮ᴰ-S : DUARel 𝒮-A S ℓ≅S) (πS≅ : ∀ {a} {r : R a} {e} {r' : R a} → r ≅R⟨ e ⟩ r' → DUARel._≅ᴰ⟨_⟩_ 𝒮ᴰ-S (πS r) e (πS r')) → Typeω where -- `fields:` -- Base case, no fields yet recorded in `𝒮ᴰ-S`. fields: : DUAFields 𝒮-A R _≅R⟨_⟩_ (λ _ → tt) (𝒮ᴰ-Unit 𝒮-A) (λ _ → tt) -- `… data[ πF ∣ 𝒮ᴰ-F ∣ πF≅ ]` -- Add a new field with a DURG. `πF` should be the name of the field in the structure record `R` and `πF≅` -- the name of the corresponding field in the equivalence record `_≅R⟨_⟩_`, while `𝒮ᴰ-F` is a DURG for the -- field's type over `𝒮-A`. Data fields that depend on previous fields of the record are not currently -- supported. _data[_∣_∣_] : ∀ {ℓS ℓ≅S} {S : A → Type ℓS} {πS : ∀ {a} → R a → S a} {𝒮ᴰ-S : DUARel 𝒮-A S ℓ≅S} {πS≅ : ∀ {a} {r : R a} {e} {r' : R a} → r ≅R⟨ e ⟩ r' → DUARel._≅ᴰ⟨_⟩_ 𝒮ᴰ-S (πS r) e (πS r')} → DUAFields 𝒮-A R _≅R⟨_⟩_ πS 𝒮ᴰ-S πS≅ → ∀ {ℓF ℓ≅F} {F : A → Type ℓF} (πF : ∀ {a} → (r : R a) → F a) (𝒮ᴰ-F : DUARel 𝒮-A F ℓ≅F) (πF≅ : ∀ {a} {r : R a} {e} {r' : R a} (p : r ≅R⟨ e ⟩ r') → DUARel._≅ᴰ⟨_⟩_ 𝒮ᴰ-F (πF r) e (πF r')) → DUAFields 𝒮-A R _≅R⟨_⟩_ (λ r → πS r , πF r) (𝒮ᴰ-S ×𝒮ᴰ 𝒮ᴰ-F) (λ p → πS≅ p , πF≅ p) -- `… prop[ πF ∣ propF ]` -- Add a new propositional field. `πF` should be the name of the field in the structure record `R`, while -- propF is a proof that this field is a proposition. _prop[_∣_] : ∀ {ℓS ℓ≅S} {S : A → Type ℓS} {πS : ∀ {a} → R a → S a} {𝒮ᴰ-S : DUARel 𝒮-A S ℓ≅S} {πS≅ : ∀ {a} {r : R a} {e} {r' : R a} → r ≅R⟨ e ⟩ r' → DUARel._≅ᴰ⟨_⟩_ 𝒮ᴰ-S (πS r) e (πS r')} → DUAFields 𝒮-A R _≅R⟨_⟩_ πS 𝒮ᴰ-S πS≅ → ∀ {ℓF} {F : (a : A) → S a → Type ℓF} (πF : ∀ {a} → (r : R a) → F a (πS r)) (propF : ∀ a s → isProp (F a s)) → DUAFields 𝒮-A R _≅R⟨_⟩_ (λ r → πS r , πF r) (𝒮ᴰ-subtype 𝒮ᴰ-S propF) (λ p → πS≅ p)
|
data
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Function",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Path",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.List as List",
"open import Cubical.Data.Unit",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Maybe as Maybe",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Properties",
"open import Cubical.Displayed.Prop",
"open import Cubical.Displayed.Sigma",
"open import Cubical.Displayed.Unit",
"open import Cubical.Displayed.Universe",
"open import Cubical.Displayed.Auto",
"import Agda.Builtin.Reflection as R",
"open import Cubical.Reflection.Base",
"import Cubical.Reflection.RecordEquiv as RE"
] |
Cubical/Displayed/Record.agda
|
DUAFields
| |
SubstRel {A : Type ℓA} {ℓ≅A : Level} (𝒮-A : UARel A ℓ≅A) (B : A → Type ℓB) : Type (ℓ-max (ℓ-max ℓA ℓB) ℓ≅A) where no-eta-equality constructor substrel open UARel 𝒮-A field act : {a a' : A} → a ≅ a' → B a ≃ B a' uaˢ : {a a' : A} (p : a ≅ a') (b : B a) → subst B (≅→≡ p) b ≡ equivFun (act p) b uaˢ⁻ : {a a' : A} (p : a ≅ a') (b : B a') → subst B (sym (≅→≡ p)) b ≡ invEq (act p) b uaˢ⁻ p b = subst B (sym (≅→≡ p)) b ≡⟨ cong (subst B (sym (≅→≡ p))) (sym (secEq (act p) b)) ⟩ subst B (sym (≅→≡ p)) (equivFun (act p) (invEq (act p) b)) ≡⟨ cong (subst B (sym (≅→≡ p))) (sym (uaˢ p (invEq (act p) b))) ⟩ subst B (sym (≅→≡ p)) (subst B (≅→≡ p) (invEq (act p) b)) ≡⟨ pathToIso (cong B (≅→≡ p)) .Iso.ret (invEq (act p) b) ⟩ invEq (act p) b ∎ Subst→DUA : {A : Type ℓA} {ℓ≅A : Level} {𝒮-A : UARel A ℓ≅A} {B : A → Type ℓB} → SubstRel 𝒮-A B → DUARel 𝒮-A B ℓB DUARel._≅ᴰ⟨_⟩_ (Subst→DUA 𝒮ˢ-B) b p b' = equivFun (SubstRel.act 𝒮ˢ-B p) b ≡ b' DUARel.uaᴰ (Subst→DUA {𝒮-A = 𝒮-A} {B = B} 𝒮ˢ-B) b p b' = equivFun (SubstRel.act 𝒮ˢ-B p) b ≡ b' ≃⟨ invEquiv (compPathlEquiv (sym (SubstRel.uaˢ 𝒮ˢ-B p b))) ⟩ subst B (≅→≡ p) b ≡ b' ≃⟨ invEquiv (PathP≃Path (λ i → B (≅→≡ p i)) b b') ⟩ PathP (λ i → B (≅→≡ p i)) b b' ■ where open UARel 𝒮-A
|
record
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Path",
"open import Cubical.Foundations.Transport",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Displayed.Base"
] |
Cubical/Displayed/Subst.agda
|
SubstRel
| |
𝒮-Unit : UARel Unit ℓ-zero
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Data.Unit",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Constant"
] |
Cubical/Displayed/Unit.agda
|
𝒮-Unit
| |
𝒮ᴰ-Unit : {A : Type ℓA} (𝒮-A : UARel A ℓ≅A) → DUARel 𝒮-A (λ _ → Unit) ℓ-zero
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.HLevels",
"open import Cubical.Data.Unit",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Constant"
] |
Cubical/Displayed/Unit.agda
|
𝒮ᴰ-Unit
| |
𝒮-Univ : ∀ ℓ → UARel (Type ℓ) ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Universe.agda
|
𝒮-Univ
| |
𝒮ˢ-El : ∀ ℓ → SubstRel (𝒮-Univ ℓ) (λ X → X)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Universe.agda
|
𝒮ˢ-El
| |
𝒮ᴰ-El : ∀ ℓ → DUARel (𝒮-Univ ℓ) (λ X → X) ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Foundations.Isomorphism",
"open import Cubical.Foundations.Univalence",
"open import Cubical.Displayed.Base",
"open import Cubical.Displayed.Subst"
] |
Cubical/Displayed/Universe.agda
|
𝒮ᴰ-El
| |
Fin : ℕ → FinSet ℓ-zero
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
Fin
| |
s2 : card (_ , isFinSet≃ (Fin 2) (Fin 2)) ≡ 2
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
s2
| |
s3 : card (_ , isFinSet≃ (Fin 3) (Fin 3)) ≡ 6
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
s3
| |
getFun : {n : ℕ} → Vec ℕ n → Fin n .fst → ℕ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
getFun
| |
s : sum (Fin _) f ≡ 31
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
s
| |
p : prod (Fin _) f ≡ 6480
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
p
| |
m : maxValue (Fin _) f ∣ fzero ∣ ≡ 9
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
m
| |
n1 : card (_ , isFinSetFiberDisc (Fin _) ℕ discreteℕ f 1) ≡ 2
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
n1
| |
R : {n : ℕ} → Fin n .fst → Fin n .fst → Type
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
R
| |
isDecR : {n : ℕ} → (x y : Fin n .fst) → isDecProp (R {n = n} x y)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
isDecR
| |
isEquivRelR : {n : ℕ} → isEquivRel (R {n = n})
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
isEquivRelR
| |
collapsed : (n : ℕ) → FinSet ℓ-zero
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Nat.Order",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sum",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.Vec",
"open import Cubical.Data.SumFin renaming (Fin to Fin')",
"open import Cubical.Data.FinSet.Base",
"open import Cubical.Data.FinSet.Properties",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinSet.Cardinality",
"open import Cubical.Data.FinSet.DecidablePredicate",
"open import Cubical.Data.FinSet.Quotients",
"open import Cubical.HITs.PropositionalTruncation",
"open import Cubical.Relation.Nullary",
"open import Cubical.Relation.Nullary.DecidablePropositions",
"open import Cubical.Relation.Binary",
"open import Cubical.Functions.Embedding",
"open import Cubical.Functions.Surjection"
] |
Cubical/Experiments/Combinatorics.agda
|
collapsed
| |
https : //github.com/EgbertRijke/OEIS-A000001
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Data.FinSet.Induction",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinType",
"open import Cubical.Data.FinType.FiniteStructure"
] |
Cubical/Experiments/CountingFiniteStructure.agda
|
https
| |
isFinStrCard : (S : FinSet ℓ-zero → FinSet ℓ) (n : ℕ) → isFinType 0 (FinSetWithStrOfCard S n)
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Data.FinSet.Induction",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinType",
"open import Cubical.Data.FinType.FiniteStructure"
] |
Cubical/Experiments/CountingFiniteStructure.agda
|
isFinStrCard
| |
TrivialStr : FinSet ℓ → FinSet ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Data.FinSet.Induction",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinType",
"open import Cubical.Data.FinType.FiniteStructure"
] |
Cubical/Experiments/CountingFiniteStructure.agda
|
TrivialStr
| |
IdentityStr : FinSet ℓ → FinSet ℓ
|
function
|
Cubical
|
[
"open import Cubical.Foundations.Prelude",
"open import Cubical.Foundations.Equiv",
"open import Cubical.Data.Nat",
"open import Cubical.Data.Bool",
"open import Cubical.Data.Sigma",
"open import Cubical.Data.FinSet",
"open import Cubical.Data.FinSet.Induction",
"open import Cubical.Data.FinSet.Constructors",
"open import Cubical.Data.FinType",
"open import Cubical.Data.FinType.FiniteStructure"
] |
Cubical/Experiments/CountingFiniteStructure.agda
|
IdentityStr
|
End of preview. Expand
in Data Studio
Agda-Cubical
Structured dataset from agda/cubical — Cubical Agda library for HoTT and univalent mathematics.
3,028 declarations extracted from Agda source files.
Applications
- Training language models on formal proofs
- Fine-tuning theorem provers
- Retrieval-augmented generation for proof assistants
- Learning proof embeddings and representations
Source
- Repository: https://github.com/agda/cubical
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Declaration body |
| type | string | data, record, function |
| library | string | Source module |
| imports | list | Required imports |
| filename | string | Source file path |
| symbolic_name | string | Identifier |
- Downloads last month
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Size of downloaded dataset files:
300 kB
Size of the auto-converted Parquet files:
300 kB
Number of rows:
3,028