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dlicata335 committed Sep 7, 2016
1 parent bb1dca0 commit a1f3307
Showing 1 changed file with 2 additions and 3 deletions.
5 changes: 2 additions & 3 deletions misc/UABetaOnly-SelfContained.agda
Original file line number Diff line number Diff line change
Expand Up @@ -102,7 +102,7 @@ module misc.UABetaOnly-SelfContained where
Equiv : {l1 l2 : Level} Set l1 Set l2 Set (l1 ⊔ l2)
Equiv A B = Σ (IsEquiv{A = A}{B})

-- from Martin Escardo on HoTT book list
-- from Martin Escardo on HoTT book list https://github.com/HoTT/book/issues/718
retract-of-Id-is-Id : {l1 l2 : Level} {A : Set l1} {R : A A Set l2}
(r : {x y : A} x == y -> R x y)
(s : {x y : A} R x y x == y)
Expand All @@ -129,9 +129,8 @@ module misc.UABetaOnly-SelfContained where
full : {B X} IsEquiv {_}{_} {B == X} {Equiv B X} (coe-equiv)
full = retract-of-Id-is-Id coe-equiv ua (λ c pair≃ (uaβ c) ((IsEquiv-HProp _) _ _))


module TheCanonicalMap (λ= : {l1 l2 : Level} {A : Set l1} {B : A -> Set l2} {f g : (x : A) -> B x} -> ((x : A) -> Path (f x) (g x)) -> Path f g) where
-- assuming we have function extensionality (or using the above to get it),
-- assuming we have function extensionality (if not we can use the above to get it?),
-- we can show that this is the same map as VV canonical map

id-equiv : {l : Level} {A : Set l} -> Equiv A A
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