mirror of https://github.com/nmvdw/HITs-Examples
50 lines
1.3 KiB
Plaintext
50 lines
1.3 KiB
Plaintext
{-# OPTIONS --without-K --rewriting #-}
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open import HoTT
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module Interval where
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postulate
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I : Set
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z : I
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o : I
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s : z == o
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I-ind : (Y : I -> Set)
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(zY : Y z)
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(oY : Y o)
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(sY : PathOver Y s zY oY)
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(x : I)
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-> Y x
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I-ind-βz : (Y : I -> Set)
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(zY : Y z)
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(oY : Y o)
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(sY : PathOver Y s zY oY)
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-> I-ind Y zY oY sY z ↦ zY
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{-# REWRITE I-ind-βz #-}
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I-ind-βo : (Y : I -> Set)
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(zY : Y z)
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(oY : Y o)
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(sY : PathOver Y s zY oY)
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-> I-ind Y zY oY sY o ↦ oY
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{-# REWRITE I-ind-βo #-}
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I-ind-βs : (Y : I -> Set)
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(zY : Y z)
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(oY : Y o)
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(sY : PathOver Y s zY oY)
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-> apd (I-ind Y zY oY sY) s == sY
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transp-cst : (A : Set) {x y : A} (B : Set) (p : x == y) (z : B) -> transport (\x -> B) p z == z
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transp-cst A B idp z = idp
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transp-fun : (A B : Set) (a b : A) (p : a == b) (f : A -> B) -> transport (λ _ -> A -> B) p f == transport (λ _ -> B) p (f a)
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transp-fun = ?
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fe : {A B : Set} (f g : A -> B) -> ( (x : A) -> f x == g x) -> f == g
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fe {A} {B} f g p =
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ap
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(I-ind (λ _ → (x : A) → B) f g
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(from-transp (λ _ → (x : A) → B) s (
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{!!}
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)))
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s
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