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Svstmt.lisp

Svstmt-writelist-vars

Signature
(svstmt-writelist-vars x) → vars
Arguments: x — Guard (svstmt-writelist-p x).
Returns: vars — Type (svarlist-p vars).

Definitions and Theorems

Function: svstmt-writelist-vars

(defun svstmt-writelist-vars (x)
  (declare (xargs :guard (svstmt-writelist-p x)))
  (let ((__function__ 'svstmt-writelist-vars))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (append-without-guard (svstmt-write-vars (car x))
                            (svstmt-writelist-vars (cdr x))))))

Theorem: svarlist-p-of-svstmt-writelist-vars

(defthm svarlist-p-of-svstmt-writelist-vars
  (b* ((vars (svstmt-writelist-vars x)))
    (svarlist-p vars))
  :rule-classes :rewrite)

Theorem: svstmt-writelist-vars-of-svstmt-writelist-fix-x

(defthm svstmt-writelist-vars-of-svstmt-writelist-fix-x
  (equal (svstmt-writelist-vars (svstmt-writelist-fix x))
         (svstmt-writelist-vars x)))

Theorem: svstmt-writelist-vars-svstmt-writelist-equiv-congruence-on-x

(defthm svstmt-writelist-vars-svstmt-writelist-equiv-congruence-on-x
  (implies (svstmt-writelist-equiv x x-equiv)
           (equal (svstmt-writelist-vars x)
                  (svstmt-writelist-vars x-equiv)))
  :rule-classes :congruence)