This directory contains some books featured in the chapter "Continuity
and Differentiability in ACL2" of the book "Computer-Aided Reeasoning:
ACL2 Case Studies," by Ruben Gamboa.  In particular, the books develop
the elementary theory of continuous and differentiable functions.
Some of the development was left off as exercises in the chapter, and
this directory contains the author's solutions.

The books here serve to describe the non-standard extensions to ACL2,
which are incorporated in ACL2(r).  (See also the documentation topic
REAL for information about ACL2(r).)  Users who wish to pursue this
area further are advised to consult the ACL2(r) book nsa (see
../../nonstd/nsa/nsa.lisp), which proves many useful theorems from
non-standard analysis.

NOTE:  These books are intended NOT to be certified here.  To certify
them, work in the "mirrored" copy of this directory, which under the
ACL2 distribution resides in books/nonstd/case-studies/analysis/
(i.e., relative to the present directory is
../../nonstd/case-studies/analysis/).  See ../../nonstd/README for
important instructions.

    * continuity.lisp		-- Intermediate-value theorem

    * derivatives.lisp		-- Rolle's theorem, mean-value theorem

    * exercise1.lisp		-- The non-existence of sqrt(2) in ACL2,
	                           and/or its irrationality in ACL2(r).

    * exercise2.lisp            -- A different version of the intermediate-
	                           value theorem.

    * exercise3.lisp		-- Uses the intermediate-value theorem to
				   show the existence of sqrt(2) in ACL2(r).

    * exercise4.lisp		-- Finds the maximum point for a continuous
				   function over a closed bounded interval.

    * exercise5.lisp		-- Finds the minimum point for a continuous
				   function over a closed bounded interval.

    * exercise6.lisp		-- The sum/product of two continuous functions
				   is continuous.

    * exercise7.lisp		-- Proves the classical version of Rolle's
				   theorem.

    * exercise8.lisp		-- The sum/product of two differentiable 
				   functions is differentiable.
		

