[jblezo]

Also, I'm not sure that those two affirmations are equivalent:

  ~∀x  (~IsAHatOfMine(x) ∨  Green(x))

   ∃x ~(~IsAHatOfMine(x) ∨  Green(x))

[FabHK]

That's basically "infinite" DeMorgan:

https://en.wikipedia.org/wiki/De_Morgan's_laws#Extension_to_...