stuck again

This commit is contained in:
Michael Zhang 2023-05-17 03:57:06 -05:00
parent ae0452715b
commit 98c5b14e06
Signed by: michael
GPG key ID: BDA47A31A3C8EE6B

View file

@ -56,18 +56,50 @@ center-fiber-is-contr y fz =
pz : convert z y
pz = proj₂ fz
eqv3 : convert x convert z
eqv3 = px sym pz
un-ap-convert : (a b : Bool) (p : convert a convert b) a b
un-ap-convert a b p =
let inner = ap convert-inv p in
sym (convert-inv-id a) inner convert-inv-id b
eqv4 : convert-inv (convert x) convert-inv (convert z)
eqv4 = ap convert-inv eqv3
cx≡cz : convert x convert z
cx≡cz = px sym pz
-- eqv4 : convert-inv (convert x) ≡ convert-inv (convert z)
-- eqv4 = ap convert-inv cx≡cz
x≡z : x z
x≡z = sym (convert-inv-id x) eqv4 convert-inv-id z
-- x≡z = sym (convert-inv-id x) ∙ eqv4 ∙ convert-inv-id z
x≡z = un-ap-convert x z cx≡cz
P : Bool Type
P b = convert b y
-- Using subst here because that's what Σ-≡,≡→≡ uses
px≡pz : (subst P x≡z px) pz
px≡pz = J
(λ b p
let
x≡b : x b
x≡b = ?
convert-the : convert b y
convert-the = ?
in
(subst P x≡b px) convert-the
) x≡z refl
give-me-info = ?
in
Σ-≡,≡→≡ (x≡z , ?)
-- Goal type:
-- transport (λ cx → convert cx ≡ y)
-- (
-- sym (convert-inv-id x)
-- ∙ ap convert-inv (px ∙ sym pz)
-- ∙ convert-inv-id z
-- )
-- (proj₂ (center-fiber y)) <-- this is just px
-- ≡ proj₂ fz <-- this is just pz
Σ-≡,≡→≡ (x≡z , px≡pz)
convert-is-equiv : isEquiv convert
convert-is-equiv .equiv-proof y = center-fiber y , center-fiber-is-contr y