Definition:Immediate Predecessor Element

Let $$\left({S; \preceq}\right)$$ be a poset.

Let $$a, b \in S$$.

Then $$a$$ is the predecessor to $$b$$ iff:
 * 1) $$a \prec b$$;
 * 2) $$\lnot \exists c \in S: a \prec c \prec b$$.

We say that $$a$$ immediately precedes $$b$$.