[Haskell-beginners] Trying to prove Applicative is superclass of Functor, etc

[Silent Leaf]

Hi, well aware it's trivial so I'll be terse: do we have?:
> fmap = <*> . pure
So we could write for example
> liftA2 f fa fb =  f <$> fa <*> fb
this way?:
> liftA2 f fa fb = pure f <*> fa <*> fb <*>

Incidentally, do we have?:
> liftA == liftM == fmap

Thanks!
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