[WIP] Scary goal

This commit is contained in:
Frederik Hanghøj Iversen 2018-03-20 11:58:54 +01:00
parent 32d1833d51
commit 30725d71b6

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@ -28,10 +28,21 @@ sym≃ = Equivalence.symmetry
infixl 10 _⊙_ infixl 10 _⊙_
module _ { : Level} {A : Set } {a : A} where module _ { : Level} {A : Set } {a : A} where
-- "This follows from the propositional equiality for `J`" - Vezzosi.
id-coe : coe refl a a id-coe : coe refl a a
id-coe = begin id-coe = begin
coe refl a ≡⟨ {!!} coe refl a ≡⟨⟩
-- pathJprop : pathJ _ refl ≡ d
pathJ (λ y x A) scary A refl ≡⟨ pathJprop {x = scary} (λ y x A) scary
scary ≡⟨ {!!}
-- pathJ (λ y x → A) scary A refl ≡⟨ pathJprop {A = A} (λ y x → A) scary ⟩
-- scary ≡⟨ {!!} ⟩
-- pathJ (λ y _ → B _ → B y) (λ x → x) _ p ≡⟨ {!!} ⟩
a a
where
scary : A
scary = (primComp (λ j A) i0 (λ j p[ a ] i0 (~ j)) a)
module _ { : Level} {A B : Set } {a : A} where module _ { : Level} {A B : Set } {a : A} where
inv-coe : (p : A B) coe (sym p) (coe p a) a inv-coe : (p : A B) coe (sym p) (coe p a) a
@ -225,7 +236,11 @@ module _ ( : Level) where
h = sym≃ (univalence {A = A} {B}) h = sym≃ (univalence {A = A} {B})
k : Σ _ (isEquiv (A B) (A B)) k : Σ _ (isEquiv (A B) (A B))
k = Eqv.doEta h k = Eqv.doEta h
in {!!} eqv : Σ (A B) (isEquiv A B) Eqv.≅ (A B)
eqv = {!!} , {!!} , {!!}
hh : Σ (A B) (isEquiv A B) (A B)
hh = Eeq.fromIsomorphism eqv
in hh h
-- lem2 with propIsSet -- lem2 with propIsSet
step2 : (A B) (hA hB) step2 : (A B) (hA hB)