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