Also, I'm not sure that those two affirmations are equivalent:
~∀x (~IsAHatOfMine(x) ∨ Green(x))
∃x ~(~IsAHatOfMine(x) ∨ Green(x)) ~∀x (~IsAHatOfMine(x) ∨ Green(x))
∃x ~(~IsAHatOfMine(x) ∨ Green(x))https://en.wikipedia.org/wiki/De_Morgan's_laws#Extension_to_...