32 lines
1.2 KiB
Text
32 lines
1.2 KiB
Text
inductive [class] fibrant (T : Type) : Type
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| fibrant_mk : fibrant
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axiom pi_fibrant {A : Type} {B : A → Type} [C1 : fibrant A] [C2 : Πx : A, fibrant (B x)] :
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fibrant (Πx : A, B x)
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attribute pi_fibrant [instance]
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inductive path {A : Type} [fA : fibrant A] (a : A) : A → Type
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| idpath : path a
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axiom path_fibrant {A : Type} [fA : fibrant A] (a b : A) : fibrant (path a b)
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attribute path_fibrant [instance]
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notation a ≈ b := path a b
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noncomputable definition test {A : Type} [fA : fibrant A] {x y : A} :
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Π (z : A), y ≈ z → fibrant (x ≈ y → x ≈ z) := take z p, _
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noncomputable definition test2 {A : Type} [fA : fibrant A] {x y : A} :
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Π (z : A), y ≈ z → fibrant (x ≈ y → x ≈ z) := _
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noncomputable definition test3 {A : Type} [fA : fibrant A] {x y : A} :
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Π (z : A), y ≈ z → fibrant (x ≈ z) := _
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noncomputable definition test4 {A : Type} [fA : fibrant A] {x y z : A} :
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fibrant (x ≈ y → x ≈ z) := _
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axiom imp_fibrant {A : Type} {B : Type} [C1 : fibrant A] [C2 : fibrant B] : fibrant (A → B)
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attribute imp_fibrant [instance]
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noncomputable definition test5 {A : Type} [fA : fibrant A] {x y : A} :
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Π (z : A), y ≈ z → fibrant (x ≈ y → x ≈ z) := _
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