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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::sub (mod 1 prime) x prime)
                           (pfield::sub (mod 1 prime) y 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 (:sub (:const 1) (:var "x"))
                                       (:sub (: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))))