/usr/share/acl2-7.2dfsg/books/arithmetic/realp.lisp is in acl2-books-source 7.2dfsg-3.
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; Contributed by Ruben Gamboa
; Copyright (C) 2014, University of Wyoming
; All rights reserved.
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
;;; Surprisingly, ACL2 knows very little about the rational numbers.
;;; Even though its type system knows that x*y is rational when x and
;;; y are rational, it gets confused when a theorem has that as a
;;; hypothesis, because the crucial fact is needed by the rewriter,
;;; not the type-system. Sad, really.
;;; The arithmetic books solve this problem for the rationals. The
;;; same problems apply to ACL2(r) with the reals, so we include those
;;; simple theorems here.
#+non-standard-analysis
; [Jared] adding #+non-standard-analysis so that we can include this book in
; ordinary ACL2, and hence keep the include-book commands uniform across both
; ACL2 and ACL2(r).
(progn
(defthm realp-+
(implies (and (realp x) (realp y))
(realp (+ x y))))
(defthm realp-uminus
(implies (realp x)
(realp (- x))))
(defthm realp-*
(implies (and (realp x) (realp y))
(realp (* x y))))
(defthm realp-udiv
(implies (realp x)
(realp (/ x))))
)
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