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• Execution-executable

Stepnx

Executable multi-step execution function.

This is obtained from stepn via apt::simplify, passing step-is-stepx to propagate it. The result is the same as stepn, but with a call of stepx instead of step. The generated theorem that unconditionally rewrites stepn to stepnx is stepn-to-stepnx.

We manually propagate the fixing and state validity preservation theorems that accompany stepn to stepnx.

Definitions and Theorems

Function: stepnx

(defun stepnx (n stat feat)
  (declare (xargs :guard (and (natp n)
                              (statp stat)
                              (featp feat)
                              (stat-validp stat feat))))
  (cond ((zp n) (stat-fix stat))
        ((errorp stat feat) (stat-fix stat))
        (t (stepnx (1- n)
                   (stepx stat feat)
                   feat))))

Theorem: stepn-is-stepnx

(defthm stepn-is-stepnx
  (equal (stepn n stat feat)
         (stepnx n stat feat)))

Theorem: stepnx-of-nfix-n

(defthm stepnx-of-nfix-n
  (equal (stepnx (nfix n) stat feat)
         (stepnx n stat feat)))

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

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

Theorem: stepnx-of-stat-fix-stat

(defthm stepnx-of-stat-fix-stat
  (equal (stepnx n (stat-fix stat) feat)
         (stepnx n stat feat)))

Theorem: stepnx-stat-equiv-congruence-on-stat

(defthm stepnx-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (stepnx n stat feat)
                  (stepnx n stat-equiv feat)))
  :rule-classes :congruence)

Theorem: stepnx-of-feat-fix-feat

(defthm stepnx-of-feat-fix-feat
  (equal (stepnx n stat (feat-fix feat))
         (stepnx n stat feat)))

Theorem: stepnx-feat-equiv-congruence-on-feat

(defthm stepnx-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (stepnx n stat feat)
                  (stepnx n stat feat-equiv)))
  :rule-classes :congruence)

Theorem: stat-validp-of-stepnx

(defthm stat-validp-of-stepnx
  (implies (stat-validp stat feat)
           (stat-validp (stepnx n stat feat)
                        feat)))