That's it, there are no more basic rules. Well, there still exist some more to deal with quantifiers and two about true and false, which I will explain later, but with the former 9 we're able to try to prove the validity of any sequent in this document (except the ones with quantifiers...).
Remember again that there are no more rules: you can't change from
to
(true) directly, or from
to
, nor use the distributive,
associative or commutative property. You have to proceed always step
by step; even the simple changes aren't allowed (currently). Why?
Because probably they aren't that simple: you will understand it when
having to prove things like that
is always true...
(it's in the next section).