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@ -1631,11 +1631,11 @@ EquivJ {X} P d {Y} e = subst {(Y : Type) * Equiv Y X} (\x -> P x.1 x.2) path d w |
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path : Path {(Y : Type) * Equiv Y X} (X, the X, idEquiv {X}) (Y, e) |
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path : Path {(Y : Type) * Equiv Y X} (X, the X, idEquiv {X}) (Y, e) |
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path = isContr_isProp {(Y : Type) * Equiv Y X} contrSinglEquiv (X, the X, idEquiv {X}) (Y, e) |
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path = isContr_isProp {(Y : Type) * Equiv Y X} contrSinglEquiv (X, the X, idEquiv {X}) (Y, e) |
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pathToEquiv : {A : Type} {B : Type} -> Path A B -> Equiv A B |
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pathToEquiv {A} {B} = J {Type} {A} (\B p -> Equiv A B) (the A, idEquiv {A}) |
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uaIso : {A : Type} {B : Type} -> Iso (Path A B) (Equiv A B) |
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uaIso : {A : Type} {B : Type} -> Iso (Path A B) (Equiv A B) |
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uaIso = (pathToEquiv, univalence, pathToEquiv_univalence, univalence_pathToEquiv) where |
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uaIso = (pathToEquiv, univalence, pathToEquiv_univalence, univalence_pathToEquiv) where |
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pathToEquiv : {A : Type} {B : Type} -> Path A B -> Equiv A B |
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pathToEquiv {A} {B} = J {Type} {A} (\B p -> Equiv A B) (the A, idEquiv {A}) |
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pathToEquiv_refl : {A : Type} -> Path (pathToEquiv (refl {Type} {A})) (the A, idEquiv {A}) |
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pathToEquiv_refl : {A : Type} -> Path (pathToEquiv (refl {Type} {A})) (the A, idEquiv {A}) |
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pathToEquiv_refl {A} = JRefl (\B p -> Equiv A B) (the A, idEquiv {A}) |
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pathToEquiv_refl {A} = JRefl (\B p -> Equiv A B) (the A, idEquiv {A}) |
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