		Search-engine friendly clone of the ACL2 documentation.

Boolean-and

Boolean-and-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: boolean-and-pred

(defun boolean-and-pred (x y z prime)
  (and (equal (pfield::mul x y prime) z)))

Theorem: definition-satp-to-boolean-and-pred

(defthm definition-satp-to-boolean-and-pred
 (implies
  (and
   (equal
       (pfcs::lookup-definition '(:simple "boolean_and")
                                pfcs::defs)
       '(:definition (name :simple "boolean_and")
                     (pfcs::para (:simple "x")
                                 (:simple "y")
                                 (:simple "z"))
                     (pfcs::body (:equal (:mul (:var (:simple "x"))
                                               (:var (:simple "y")))
                                         (:var (:simple "z"))))))
   (pfield::fep x prime)
   (pfield::fep y prime)
   (pfield::fep z prime)
   (primep prime))
  (equal (pfcs::definition-satp '(:simple "boolean_and")
                                pfcs::defs (list x y z)
                                prime)
         (boolean-and-pred x y z prime))))