Induction Proofs for Recursively Defined Sets
These notes are intended to supplement the text
by giving a definition of inductive proofs for recursively defined sets.
A recursive definition of a set has three parts:
A basis telling
what elements are in the set initially;
the recursive or constructor part:
which tells how to add elements to the set given that a list of certain elements
already are in the set;
and an extremal clause which is
the legal fine print saying that all elements in the set follow
from the basis and the recursive part.