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Opcode-extension-group-p

Signature

(opcode-extension-group-p x) → *

Definitions and Theorems

Function: opcode-extension-group-p

(defun opcode-extension-group-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'opcode-extension-group-p))
    (declare (ignorable __function__))
    (or (not x)
        (and (acl2::keyword-listp x)
             (subsetp-equal x *group-numbers*)))))

Function: opcode-extension-group-fix

(defun opcode-extension-group-fix (x)
  (declare (xargs :guard (opcode-extension-group-p x)))
  (let ((__function__ 'opcode-extension-group-fix))
    (declare (ignorable __function__))
    (mbe :logic (if (opcode-extension-group-p x) x 'nil)
         :exec x)))

Function: opcode-extension-group-equiv$inline

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

Theorem: opcode-extension-group-equiv-is-an-equivalence

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

Theorem: opcode-extension-group-equiv-implies-equal-opcode-extension-group-fix-1

(defthm
 opcode-extension-group-equiv-implies-equal-opcode-extension-group-fix-1
 (implies (opcode-extension-group-equiv x x-equiv)
          (equal (opcode-extension-group-fix x)
                 (opcode-extension-group-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: opcode-extension-group-fix-under-opcode-extension-group-equiv

(defthm
      opcode-extension-group-fix-under-opcode-extension-group-equiv
  (opcode-extension-group-equiv (opcode-extension-group-fix x)
                                x)
  :rule-classes (:rewrite :rewrite-quoted-constant))