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Field-if

Field-if-spec

Specification of the circuit.

Signature
(field-if-spec x y z w prime) → yes/no
Arguments: x — Guard (pfield::fep x prime).; y — Guard (pfield::fep y prime).; z — Guard (pfield::fep z prime).; w — Guard (pfield::fep w prime).; prime — Guard (primep prime).
Returns: yes/no — Type (booleanp yes/no).

We use an if, obviously.

Definitions and Theorems

Function: field-if-spec

(defun field-if-spec (x y z w prime)
  (declare (xargs :guard (and (primep prime)
                              (pfield::fep x prime)
                              (pfield::fep y prime)
                              (pfield::fep z prime)
                              (pfield::fep w prime))))
  (declare (ignore prime))
  (declare (xargs :guard (bitp x)))
  (let ((__function__ 'field-if-spec))
    (declare (ignorable __function__))
    (equal w (if (= x 1) y z))))

Theorem: booleanp-of-field-if-spec

(defthm booleanp-of-field-if-spec
  (b* ((yes/no (field-if-spec x y z w prime)))
    (booleanp yes/no))
  :rule-classes :rewrite)