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Execution32

Step32n

Multi-step execution.

Signature
(step32n n stat) → new-stat
Arguments: n — Guard (natp n).; stat — Guard (stat32ip stat).
Returns: new-stat — Type (stat32ip 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: step32n

(defun step32n (n stat)
  (declare (xargs :guard (and (natp n) (stat32ip stat))))
  (let ((__function__ 'step32n))
    (declare (ignorable __function__))
    (cond ((zp n) (stat32i-fix stat))
          ((error32p stat) (stat32i-fix stat))
          (t (step32n (1- n) (step32 stat))))))

Theorem: stat32ip-of-step32n

(defthm stat32ip-of-step32n
  (b* ((new-stat (step32n n stat)))
    (stat32ip new-stat))
  :rule-classes :rewrite)

Theorem: step32n-of-nfix-n

(defthm step32n-of-nfix-n
  (equal (step32n (nfix n) stat)
         (step32n n stat)))

Theorem: step32n-nat-equiv-congruence-on-n

(defthm step32n-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (step32n n stat)
                  (step32n n-equiv stat)))
  :rule-classes :congruence)

Theorem: step32n-of-stat32i-fix-stat

(defthm step32n-of-stat32i-fix-stat
  (equal (step32n n (stat32i-fix stat))
         (step32n n stat)))

Theorem: step32n-stat32i-equiv-congruence-on-stat

(defthm step32n-stat32i-equiv-congruence-on-stat
  (implies (stat32i-equiv stat stat-equiv)
           (equal (step32n n stat)
                  (step32n n stat-equiv)))
  :rule-classes :congruence)