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Lhs.lisp

Lhs-overridelist-keys

Signature
(lhs-overridelist-keys x) → vars
Arguments: x — Guard (lhs-overridelist-p x).
Returns: vars — Type (svarlist-p vars).

Definitions and Theorems

Function: lhs-overridelist-keys

(defun lhs-overridelist-keys (x)
  (declare (xargs :guard (lhs-overridelist-p x)))
  (let ((__function__ 'lhs-overridelist-keys))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (append (lhs-vars (lhs-override->lhs (car x)))
              (lhs-overridelist-keys (cdr x))))))

Theorem: svarlist-p-of-lhs-overridelist-keys

(defthm svarlist-p-of-lhs-overridelist-keys
  (b* ((vars (lhs-overridelist-keys x)))
    (svarlist-p vars))
  :rule-classes :rewrite)

Theorem: lhs-overridelist-keys-of-lhs-overridelist-fix-x

(defthm lhs-overridelist-keys-of-lhs-overridelist-fix-x
  (equal (lhs-overridelist-keys (lhs-overridelist-fix x))
         (lhs-overridelist-keys x)))

Theorem: lhs-overridelist-keys-lhs-overridelist-equiv-congruence-on-x

(defthm lhs-overridelist-keys-lhs-overridelist-equiv-congruence-on-x
  (implies (lhs-overridelist-equiv x x-equiv)
           (equal (lhs-overridelist-keys x)
                  (lhs-overridelist-keys x-equiv)))
  :rule-classes :congruence)