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;;;***************************************************************
;;;An ACL2 Library of Floating Point Arithmetic
;;;David M. Russinoff
;;;Advanced Micro Devices, Inc.
;;;February, 1998
;;;***************************************************************
(in-package "ACL2")
;BOZO include less...
(include-book "log")
(include-book "float")
(include-book "trunc")
(include-book "land")
(local (include-book "bits-trunc-proofs"))
(defthm bits-trunc-2
(implies (and (= n (1+ (expo x)))
(>= x 0)
(integerp k)
(> k 0)
)
(= (trunc x k)
(* (expt 2 (- n k))
(bits x (1- n) (- n k)))))
:rule-classes ())
(defthm bits-trunc
(implies (and (>= x (expt 2 (1- n)))
(< x (expt 2 n))
(integerp x) (> x 0)
(integerp m) (>= m n)
(integerp n) (> n k)
(integerp k) (> k 0)
)
(= (trunc x k)
(land x (- (expt 2 m) (expt 2 (- n k))) n)))
:rule-classes ())
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