`F |- U`

allows us to go from `F a -> x`

to `a -> U x`

. We
can look at this as shifting the "before-advice" from the ```
F a <--F--- a
| |
v v
x ----U--> U x
```

Where `F`

is for `F`

ree and `U`

is for forgetf `U`

l.
Recall that if `F`

is free and `U`

is forgetful, then `U(F(x)) = x`

, since
adding more structure through the free functor and then stripping it away gives
us the object back. We can prove that if `U(F(x)) = x`

and `U, F`

are functors,
then we have a function `fwd: (f a -> x) -> (a -> u x)`

as:
```
f :: (f a -> x)
fmap :: (p -> q) -> (u p -> u q)
fmap :: (p -> q) -> (u ( p ) -> u q)
fmap f :: (f a -> x) -> (u (f a) -> u x)
fmap f :: (f a -> x) -> (a -> u x) [using u (f a) = a]
```