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Field-add

Field-add-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: field-add-pred

(defun field-add-pred (x y z prime)
  (and (equal (pfield::mul (pfield::add x y prime)
                           (mod 1 prime)
                           prime)
              z)))

Theorem: definition-satp-to-field-add-pred

(defthm definition-satp-to-field-add-pred
 (implies
  (and
   (equal
        (pfcs::lookup-definition "field_add" pfcs::defs)
        '(:definition
              (pfcs::name . "field_add")
              (pfcs::para "x" "y" "z")
              (pfcs::body (:equal (:mul (:add (:var "x") (:var "y"))
                                        (:const 1))
                                  (:var "z")))))
   (pfield::fep x prime)
   (pfield::fep y prime)
   (pfield::fep z prime)
   (primep prime))
  (equal (pfcs::definition-satp "field_add" pfcs::defs (list x y z)
                                prime)
         (field-add-pred x y z prime))))