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Vl-context

Vl-context-fix

Signature
(vl-context-fix x) → *

Definitions and Theorems

Function: vl-context-fix

(defun vl-context-fix (x)
  (declare (xargs :guard t))
  (let ((__function__ 'vl-context-fix))
    (declare (ignorable __function__))
    x))

Theorem: vl-context-p-of-vl-context-fix

(defthm vl-context-p-of-vl-context-fix
  (vl-context-p (vl-context-fix x)))

Theorem: vl-context-fix-when-vl-context-p

(defthm vl-context-fix-when-vl-context-p
  (implies (vl-context-p x)
           (equal (vl-context-fix x) x)))

Function: vl-context-equiv$inline

(defun vl-context-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vl-context-p acl2::x)
                              (vl-context-p acl2::y))))
  (equal (vl-context-fix acl2::x)
         (vl-context-fix acl2::y)))

Theorem: vl-context-equiv-is-an-equivalence

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

Theorem: vl-context-equiv-implies-equal-vl-context-fix-1

(defthm vl-context-equiv-implies-equal-vl-context-fix-1
  (implies (vl-context-equiv acl2::x x-equiv)
           (equal (vl-context-fix acl2::x)
                  (vl-context-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vl-context-fix-under-vl-context-equiv

(defthm vl-context-fix-under-vl-context-equiv
  (vl-context-equiv (vl-context-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))