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Lhs.lisp

Svexlist-resolve

Signature
(svexlist-resolve x) → res
Arguments: x — Guard (svexlist-p x).
Returns: res — Type (svex-p res).

Definitions and Theorems

Function: svexlist-resolve

(defun svexlist-resolve (x)
  (declare (xargs :guard (svexlist-p x)))
  (let ((__function__ 'svexlist-resolve))
    (declare (ignorable __function__))
    (if (atom x)
        (svex-z)
      (if (atom (cdr x))
          (svex-fix (car x))
        (svcall* res (car x)
                 (svexlist-resolve (cdr x)))))))

Theorem: svex-p-of-svexlist-resolve

(defthm svex-p-of-svexlist-resolve
  (b* ((res (svexlist-resolve x)))
    (svex-p res))
  :rule-classes :rewrite)

Theorem: svex-vars-of-svexlist-resolve

(defthm svex-vars-of-svexlist-resolve
  (set-equiv (svex-vars (svexlist-resolve x))
             (svexlist-vars x)))

Theorem: svexlist-resolve-of-svexlist-fix-x

(defthm svexlist-resolve-of-svexlist-fix-x
  (equal (svexlist-resolve (svexlist-fix x))
         (svexlist-resolve x)))

Theorem: svexlist-resolve-svexlist-equiv-congruence-on-x

(defthm svexlist-resolve-svexlist-equiv-congruence-on-x
  (implies (svexlist-equiv x x-equiv)
           (equal (svexlist-resolve x)
                  (svexlist-resolve x-equiv)))
  :rule-classes :congruence)