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• Modalist

Modalist->modnames

Signature

(modalist->modnames modalist) → modnames

Arguments

modalist — Guard (modalist-p modalist).

Returns

modnames — Type (modnamelist-p modnames).

Definitions and Theorems

Function: modalist->modnames

(defun modalist->modnames (modalist)
  (declare (xargs :guard (modalist-p modalist)))
  (let ((__function__ 'modalist->modnames))
    (declare (ignorable __function__))
    (alist-keys (mbe :logic (modalist-fix modalist)
                     :exec modalist))))

Theorem: modnamelist-p-of-modalist->modnames

(defthm modnamelist-p-of-modalist->modnames
  (b* ((modnames (modalist->modnames modalist)))
    (modnamelist-p modnames))
  :rule-classes :rewrite)

Theorem: member-modalist->modnames

(defthm member-modalist->modnames
  (iff (member x (modalist->modnames modalist))
       (modalist-lookup x modalist)))

Theorem: modalist->modnames-of-modalist-fix-modalist

(defthm modalist->modnames-of-modalist-fix-modalist
  (equal (modalist->modnames (modalist-fix modalist))
         (modalist->modnames modalist)))

Theorem: modalist->modnames-modalist-equiv-congruence-on-modalist

(defthm modalist->modnames-modalist-equiv-congruence-on-modalist
  (implies (modalist-equiv modalist modalist-equiv)
           (equal (modalist->modnames modalist)
                  (modalist->modnames modalist-equiv)))
  :rule-classes :congruence)