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Field-double

Field-double-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: field-double-pred

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

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

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