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Field-div-unchecked

Field-div-unchecked-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: field-div-unchecked-pred

(defun field-div-unchecked-pred (x y z prime)
  (and (equal (pfield::mul z y prime) x)))

Theorem: definition-satp-to-field-div-unchecked-pred

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