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decLinkedListEquiv Nil Nil = Yes $ BothEmpty
decLinkedListEquiv Nil (_ :: _) = No $ absurd
decLinkedListEquiv (_ :: _) Nil = No $ absurd
decLinkedListEquiv @{e} (h1 :: t1) (h2 :: t2) = assert_total $
decLinkedListEquiv Nil Nil = Yes BothEmpty
decLinkedListEquiv Nil (_::_) = No absurd
decLinkedListEquiv (_::_) Nil = No absurd
decLinkedListEquiv @{e} (h1::t1) (h2::t2) =
proofComposition (Left _) (Left _) _ = Refl
proofComposition (Left _) (Right _) _ = Refl
proofComposition (Right _) (Left _) _ = Refl
proofComposition (Left _) (Left _) _ = Refl
proofComposition (Left _) (Right _) _ = Refl
proofComposition (Right _) (Left _) _ = Refl
decEquiv False False = Yes $ BothFalse
decEquiv True True = Yes $ BothTrue
decEquiv False True = No $ absurd
decEquiv True False = No $ absurd
decEquiv False False = Yes BothFalse
decEquiv True True = Yes BothTrue
decEquiv False True = No absurd
decEquiv True False = No absurd
proofGreatestLowerBound False False False FalseLTEAny FalseLTEAny = FalseLTEAny
proofGreatestLowerBound False False True FalseLTEAny FalseLTEAny = FalseLTEAny
proofGreatestLowerBound False True False FalseLTEAny FalseLTEAny = FalseLTEAny
proofGreatestLowerBound False True True FalseLTEAny FalseLTEAny = FalseLTEAny
proofGreatestLowerBound False y z FalseLTEAny FalseLTEAny = FalseLTEAny
proofIdentity : (x : t a) -> map Builtin.identity x = x
proofComposition : (f : a -> b) -> (g : b -> c) -> (x : t a) -> map (g . f) x = map g . map f $ x
proofIdentity : (x : t a) -> Builtin.identity <$> x = x
proofComposition : (f : a -> b) -> (g : b -> c) -> (x : t a)
-> (g . f) <$> x = (g <$>) . (f <$>) $ x