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Field-inv-checked

Field-inv-checked-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: field-inv-checked-pred

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

Theorem: definition-satp-to-field-inv-checked-pred

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