stuck again
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1 changed files with 38 additions and 6 deletions
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@ -56,18 +56,50 @@ center-fiber-is-contr y fz =
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pz : convert z ≡ y
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pz = proj₂ fz
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eqv3 : convert x ≡ convert z
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eqv3 = px ∙ sym pz
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un-ap-convert : (a b : Bool) → (p : convert a ≡ convert b) → a ≡ b
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un-ap-convert a b p =
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let inner = ap convert-inv p in
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sym (convert-inv-id a) ∙ inner ∙ convert-inv-id b
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eqv4 : convert-inv (convert x) ≡ convert-inv (convert z)
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eqv4 = ap convert-inv eqv3
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cx≡cz : convert x ≡ convert z
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cx≡cz = px ∙ sym pz
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-- eqv4 : convert-inv (convert x) ≡ convert-inv (convert z)
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-- eqv4 = ap convert-inv cx≡cz
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x≡z : x ≡ z
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x≡z = sym (convert-inv-id x) ∙ eqv4 ∙ convert-inv-id z
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-- x≡z = sym (convert-inv-id x) ∙ eqv4 ∙ convert-inv-id z
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x≡z = un-ap-convert x z cx≡cz
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P : Bool → Type
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P b = convert b ≡ y
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-- Using subst here because that's what Σ-≡,≡→≡ uses
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px≡pz : (subst P x≡z px) ≡ pz
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px≡pz = J
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(λ b p′ →
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let
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x≡b : x ≡ b
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x≡b = ?
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convert-the : convert b ≡ y
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convert-the = ?
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in
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(subst P x≡b px) ≡ convert-the
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) x≡z refl
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give-me-info = ?
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in
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Σ-≡,≡→≡ (x≡z , ?)
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-- Goal type:
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-- transport (λ cx → convert cx ≡ y)
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-- (
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-- sym (convert-inv-id x)
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-- ∙ ap convert-inv (px ∙ sym pz)
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-- ∙ convert-inv-id z
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-- )
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-- (proj₂ (center-fiber y)) <-- this is just px
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-- ≡ proj₂ fz <-- this is just pz
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Σ-≡,≡→≡ (x≡z , px≡pz)
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convert-is-equiv : isEquiv convert
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convert-is-equiv .equiv-proof y = center-fiber y , center-fiber-is-contr y
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