		Search-engine friendly clone of the ACL2 documentation.

Execution64

Step64n

Multi-step execution.

Signature
(step64n n stat) → new-stat
Arguments: n — Guard (natp n).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

We perform n steps, or fewer if the error flag is or gets set. If n is 0, we return the state unchanged.

Definitions and Theorems

Function: step64n

(defun step64n (n stat)
  (declare (xargs :guard (and (natp n) (state64p stat))))
  (let ((__function__ 'step64n))
    (declare (ignorable __function__))
    (cond ((zp n) (state64-fix stat))
          ((error64p stat) (state64-fix stat))
          (t (step64n (1- n) (step64 stat))))))

Theorem: state64p-of-step64n

(defthm state64p-of-step64n
  (b* ((new-stat (step64n n stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: step64n-of-nfix-n

(defthm step64n-of-nfix-n
  (equal (step64n (nfix n) stat)
         (step64n n stat)))

Theorem: step64n-nat-equiv-congruence-on-n

(defthm step64n-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (step64n n stat)
                  (step64n n-equiv stat)))
  :rule-classes :congruence)

Theorem: step64n-of-state64-fix-stat

(defthm step64n-of-state64-fix-stat
  (equal (step64n n (state64-fix stat))
         (step64n n stat)))

Theorem: step64n-state64-equiv-congruence-on-stat

(defthm step64n-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (step64n n stat)
                  (step64n n stat-equiv)))
  :rule-classes :congruence)