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