Description: The Principle of Finite Induction (mathematical induction). Corollary
7.31 of TakeutiZaring p. 43. The simpler hypothesis shown here was
suggested in an email from "Colin" on 1-Oct-2001. The hypothesis states
that A is a set of natural numbers, zero belongs to A , and
given any member of A the member's successor also belongs to A .
The conclusion is that every natural number is in A . (Contributed by NM, 22-Feb-2004)(Proof shortened by Andrew Salmon, 27-Aug-2011)