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Boolean-nor

Boolean-nor-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: boolean-nor-pred

(defun boolean-nor-pred (x y z prime)
 (and
  (equal
      (pfield::mul (pfield::add (mod 1 prime)
                                (pfield::mul (mod -1 prime) x prime)
                                prime)
                   (pfield::add (mod 1 prime)
                                (pfield::mul (mod -1 prime) y prime)
                                prime)
                   prime)
      z)))

Theorem: definition-satp-to-boolean-nor-pred

(defthm definition-satp-to-boolean-nor-pred
 (implies
  (and
   (equal
      (pfcs::lookup-definition "boolean_nor" pfcs::defs)
      '(:definition
            (pfcs::name . "boolean_nor")
            (pfcs::para "x" "y" "z")
            (pfcs::body
                 (:equal (:mul (:add (:const 1)
                                     (:mul (:const -1) (:var "x")))
                               (:add (:const 1)
                                     (:mul (:const -1) (:var "y"))))
                         (:var "z")))))
   (pfield::fep x prime)
   (pfield::fep y prime)
   (pfield::fep z prime)
   (primep prime))
  (equal
       (pfcs::definition-satp "boolean_nor" pfcs::defs (list x y z)
                              prime)
       (boolean-nor-pred x y z prime))))