2014-11-05 02:41:27 +00:00
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inductive fibrant [class] (T : Type) : Type :=
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fibrant_mk : fibrant T
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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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2015-01-25 04:23:21 +00:00
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attribute pi_fibrant [instance]
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2014-11-05 02:41:27 +00:00
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inductive path {A : Type} [fA : fibrant A] (a : A) : A → Type :=
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idpath : path a a
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axiom path_fibrant {A : Type} [fA : fibrant A] (a b : A) : fibrant (path a b)
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2015-01-26 19:31:12 +00:00
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attribute path_fibrant [instance]
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2014-11-05 02:41:27 +00:00
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notation a ≈ b := path a b
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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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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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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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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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2015-01-25 04:23:21 +00:00
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attribute imp_fibrant [instance]
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2014-11-05 02:41:27 +00:00
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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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