Why are the definitions for {all,any}-of-{all,any} so complicated?

[Roland Illig <roland.illig@gmx.de>]

Hi,

I'm wondering what prevents you from using these simple definitions 
instead of the Haskell ones:

all-of(f, x, B) := \forall b \in B: f(x, b)
any-of(f, x, M) := \exists b \in B: f(x, b)
all-of-all(f, B, C) := \forall b \in B: \forall c \in C: f(b, c)
all-of-any(f, B, C) := \forall b \in B: \exists c \in C: f(b, c)
any-of-all(f, B, C) := \exists b \in B: \forall c \in C: f(b, c)
any-of-any(f, B, C) := \exists b \in B: \exists c \in C: f(b, c)

Roland