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|
(in-package "ACL2")
; cert_param: (non-acl2r)
(local (include-book "predicate"))
(defthm rationalp-product-when-one-arg-is-rational
(implies (and (rationalp x)
(case-split (not (equal x 0)))
(case-split (acl2-numberp y))
)
(and (equal (rationalp (* x y))
(rationalp y))
(equal (rationalp (* y x))
(rationalp y)))))
(defthm rationalp-sum-when-one-arg-is-rational
(implies (and (rationalp x)
(case-split (acl2-numberp y)))
(and (equal (rationalp (+ x y))
(rationalp y))
(equal (rationalp (+ y x))
(rationalp y)))))
(defthm rationalp-unary-divide
(implies (case-split (acl2-numberp x))
(equal (rationalp (/ x))
(rationalp x))))
#|
(defthm rationalp-*-when-first-factor-is-rat
(implies (and (rationalp x)
(case-split (not (equal x 0))) ;if x is 0, then...
)
(equal (rationalp (* x y))
(not (complex-rationalp y)))))
(thm
(implies (and (rationalp x)
(case-split (not (equal x 0))) ;if x is 0, then...
)
(equal (rationalp (* x y))
(not (complex-rationalp y)))))
|#
;try
(defthm rationalp-product
(implies (and (case-split (not (complex-rationalp x)))
(case-split (not (complex-rationalp y))))
(rationalp (* x y))))
|
