33 lines
1.1 KiB
Text
33 lines
1.1 KiB
Text
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open is_trunc
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inductive trunc (n : trunc_index) (A : Type) : Type :=
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tr {} : A → trunc n A
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axiom is_trunc_tr (n : trunc_index) (A : Type) : is_trunc n (trunc n A)
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attribute is_trunc_tr [instance]
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namespace trunc
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definition trunc_rec_on {n : trunc_index} {A : Type} {P : trunc n A → Type} (aa : trunc n A)
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[Pt : Πaa, is_trunc n (P aa)] (H : Πa, P (tr a)) : P aa :=
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trunc.rec_on aa H
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definition trunc_functor1 {X Y : Type} (n : trunc_index) (f : X → Y) : trunc n X → trunc n Y :=
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begin
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intro xx,
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apply (trunc_rec_on xx),
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intro x,
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exact (tr (f x))
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end
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definition trunc_functor2 {X Y : Type} (n : trunc_index) (f : X → Y) : trunc n X → trunc n Y :=
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by intro xx; exact (trunc_rec_on xx (λx, (tr (f x))))
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definition trunc_functor3 {X Y : Type} (n : trunc_index) (f : X → Y) : trunc n X → trunc n Y :=
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by exact (λxx, trunc_rec_on xx (λx, tr (f x)))
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definition trunc_functor4 {X Y : Type} (n : trunc_index) (f : X → Y) : trunc n X → trunc n Y :=
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by intro xx; apply (trunc_rec_on xx); intro x; exact (tr (f x))
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end trunc
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