[Haskell-cafe] Question, re: Typeclassopedia Ex. 4.2.1

Hi all, In trying to solve exercise 4.2.1 in Typeclassopedia, I’ve come up with the following: To prove: pure f <*> x = pure (flip ($)) <*> x <*> pure f Proof: pure (flip ($)) <*> x <*> pure f = (interchange) pure (flip ($)) <*> pure ($ f) <*> x = (homomorphism) pure (flip ($) ($ f)) <*> x = (definition of flip) pure ($ ($ f)) <*> x = (interchange) x <*> pure ($ f) = (interchange) (Is this step valid?) pure f <*> x Is the last step in my proof valid? Thanks, -db