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Mnemonic-p

Signature
(mnemonic-p x) → *

Definitions and Theorems

Function: mnemonic-p

(defun mnemonic-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'mnemonic-p))
    (declare (ignorable __function__))
    (or (stringp x) (keywordp x))))

Function: mnemonic-fix

(defun mnemonic-fix (x)
  (declare (xargs :guard (mnemonic-p x)))
  (let ((__function__ 'mnemonic-fix))
    (declare (ignorable __function__))
    (mbe :logic (if (mnemonic-p x) x ':none)
         :exec x)))

Theorem: mnemonic-p-of-mnemonic-fix

(defthm mnemonic-p-of-mnemonic-fix
  (mnemonic-p (mnemonic-fix x)))

Function: mnemonic-equiv$inline

(defun mnemonic-equiv$inline (x y)
  (declare (xargs :guard (and (mnemonic-p x) (mnemonic-p y))))
  (equal (mnemonic-fix x)
         (mnemonic-fix y)))

Theorem: mnemonic-equiv-is-an-equivalence

(defthm mnemonic-equiv-is-an-equivalence
  (and (booleanp (mnemonic-equiv x y))
       (mnemonic-equiv x x)
       (implies (mnemonic-equiv x y)
                (mnemonic-equiv y x))
       (implies (and (mnemonic-equiv x y)
                     (mnemonic-equiv y z))
                (mnemonic-equiv x z)))
  :rule-classes (:equivalence))

Theorem: mnemonic-equiv-implies-equal-mnemonic-fix-1

(defthm mnemonic-equiv-implies-equal-mnemonic-fix-1
  (implies (mnemonic-equiv x x-equiv)
           (equal (mnemonic-fix x)
                  (mnemonic-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: mnemonic-fix-under-mnemonic-equiv

(defthm mnemonic-fix-under-mnemonic-equiv
  (mnemonic-equiv (mnemonic-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))