fact stringlengths 5 16.9k | type stringclasses 3
values | library stringclasses 1
value | imports listlengths 1 62 | filename stringclasses 545
values | symbolic_name stringlengths 1 34 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
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.Algeb... | 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.Algeb... | 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.Algeb... | 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... | 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.Algeb... | 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.HLeve... | 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.HLeve... | 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.HLeve... | 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.HLeve... | 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.Structu... | 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.Structu... | Cubical/Algebra/SymmetricGroup.agda | 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 Cubic... | 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 Cubic... | 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 Cubic... | 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 Cubic... | 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",
"ope... | 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",
"ope... | 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",
"ope... | 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",
"ope... | 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",
"ope... | 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",
"ope... | 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",
"ope... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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",
"... | 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 Cub... | 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 Cub... | 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 Cub... | 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 Cub... | 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 Cub... | 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 Cub... | 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 Cub... | 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 (su... | 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.Fu... | 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 (s... | 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.Fu... | 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.... | 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.... | 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.... | 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.... | 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 im... | 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 im... | 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 im... | 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 im... | 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 im... | 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.Transpo... | 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.Transpo... | 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.Transpo... | 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.Transpo... | 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.Transpo... | 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.Propositiona... | 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.Propositiona... | 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.Embed... | 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... | 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... | 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... | 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... | 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/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 ≅... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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 Cu... | 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.Constr... | 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.Constr... | 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.Constr... | 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.Constr... | Cubical/Experiments/CountingFiniteStructure.agda | IdentityStr |
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