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Prime-fix

Fixer for dm::primep.

Function: prime-fix

(defun prime-fix (x)
  (declare (xargs :guard (dm::primep x)))
  (mbe :logic (if (dm::primep x) x 2)
       :exec x))

Theorem: primep-of-prime-fix

(defthm primep-of-prime-fix
  (b* ((fixed-x (prime-fix x)))
    (dm::primep fixed-x))
  :rule-classes :rewrite)

Theorem: prime-fix-when-primep

(defthm prime-fix-when-primep
  (implies (dm::primep x)
           (equal (prime-fix x) x)))

Theorem: posp-of-prime-fix

(defthm posp-of-prime-fix
  (posp (prime-fix x)))