Let's say I have TRUE and FALSE defined as follows:
$$\pmb{T} = \lambda ab.a$$ $$\pmb{F} = \lambda ab.b$$
Now I can define a NOT as something like the following:
$$\pmb{N} = \lambda p.p F T$$
My question is if I were to substitute in the T and F, how would I properly reduce that function? For example:
\begin{align} \pmb{N} & = \lambda p.p F T \\ & = \lambda p.p (\lambda ab.a) (\lambda ab.b) \end{align}
How does it get reduced from there?
(And on another note, is there a way to (1) align the equations in TeX so the N will be left-aligned? and (2) is there a way to put italic comments to the right of the equation to show what I'm doing in that step?)