Make progress with univalence in product-category

This commit is contained in:
Frederik Hanghøj Iversen 2018-04-12 13:16:25 +02:00
parent 7fcd8e631a
commit 5bbb40b664

View file

@ -250,8 +250,31 @@ module Try0 {a b : Level} { : Category a b}
((X , xa , xb) (Y , ya , yb)) ((X , xa , xb) (Y , ya , yb))
step2 step2
= ( λ{ ((f , f~ , inv-f) , p , q) = ( λ{ ((f , f~ , inv-f) , p , q)
( f , {!.9-1-9'!} , {!!})
, ( f~ , {!!} , {!!}) let
r : X Y
r = .isoToId (f , f~ , inv-f)
r-arrow : (.Arrow X A) (.Arrow Y A)
r-arrow i = .Arrow (r i) A
t : coe r-arrow xa .identity .<<< xa .<<< f~
t = {!? ≡ ?!}
lem : {x} .idToIso _ _ (.isoToId x) x
lem {x} i = snd .inverse-from-to-iso' i x
h : ya xa .<<< f~
h = begin
ya ≡⟨ {!!}
coe r-arrow xa
≡⟨ .9-1-9 r refl xa
fst (.idToIso _ _ refl) .<<< xa .<<< fst (snd (.idToIso _ _ r))
≡⟨ cong (λ φ φ .<<< xa .<<< fst (snd (.idToIso _ _ r))) (subst-neutral {P = λ x .Arrow x x})
.identity .<<< xa .<<< fst (snd (.idToIso _ _ r))
≡⟨ cong (λ φ .identity .<<< xa .<<< φ) (cong (λ x (fst (snd x))) lem)
.identity .<<< xa .<<< f~
≡⟨ cong (._<<< f~) .leftIdentity
xa .<<< f~
in
( f , {!h!} , {!!})
, ( f~ , sym h , {!!})
, lemA (fst inv-f) , lemA (fst inv-f)
, lemA (snd inv-f) , lemA (snd inv-f)
} }