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decLinkedListEquiv Nil Nil = Yes BothEmptydecLinkedListEquiv Nil (_::_) = No absurddecLinkedListEquiv (_::_) Nil = No absurddecLinkedListEquiv @{e} (h1::t1) (h2::t2) =
proofComposition (Left _) (Left _) _ = ReflproofComposition (Left _) (Right _) _ = ReflproofComposition (Right _) (Left _) _ = Refl
proofComposition (Left _) (Left _) _ = ReflproofComposition (Left _) (Right _) _ = ReflproofComposition (Right _) (Left _) _ = Refl
decEquiv False False = Yes $ BothFalsedecEquiv True True = Yes $ BothTruedecEquiv False True = No $ absurddecEquiv True False = No $ absurd
decEquiv False False = Yes BothFalsedecEquiv True True = Yes BothTruedecEquiv False True = No absurddecEquiv True False = No absurd
proofGreatestLowerBound False False False FalseLTEAny FalseLTEAny = FalseLTEAnyproofGreatestLowerBound False False True FalseLTEAny FalseLTEAny = FalseLTEAnyproofGreatestLowerBound False True False FalseLTEAny FalseLTEAny = FalseLTEAnyproofGreatestLowerBound False True True FalseLTEAny FalseLTEAny = FalseLTEAny
proofGreatestLowerBound False y z FalseLTEAny FalseLTEAny = FalseLTEAny
proofIdentity : (x : t a) -> map Builtin.identity x = xproofComposition : (f : a -> b) -> (g : b -> c) -> (x : t a) -> map (g . f) x = map g . map f $ x
proofIdentity : (x : t a) -> Builtin.identity <$> x = xproofComposition : (f : a -> b) -> (g : b -> c) -> (x : t a)-> (g . f) <$> x = (g <$>) . (f <$>) $ x