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• Vl-elabinstruction

Vl-elabinstruction-equiv

Basic equivalence relation for vl-elabinstruction structures.

Definitions and Theorems

Function: vl-elabinstruction-equiv$inline

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

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

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

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

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

Theorem: vl-elabinstruction-fix-under-vl-elabinstruction-equiv

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

Theorem: equal-of-vl-elabinstruction-fix-1-forward-to-vl-elabinstruction-equiv

(defthm
 equal-of-vl-elabinstruction-fix-1-forward-to-vl-elabinstruction-equiv
 (implies (equal (vl-elabinstruction-fix acl2::x)
                 acl2::y)
          (vl-elabinstruction-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-vl-elabinstruction-fix-2-forward-to-vl-elabinstruction-equiv

(defthm
 equal-of-vl-elabinstruction-fix-2-forward-to-vl-elabinstruction-equiv
 (implies (equal acl2::x
                 (vl-elabinstruction-fix acl2::y))
          (vl-elabinstruction-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: vl-elabinstruction-equiv-of-vl-elabinstruction-fix-1-forward

(defthm vl-elabinstruction-equiv-of-vl-elabinstruction-fix-1-forward
 (implies (vl-elabinstruction-equiv (vl-elabinstruction-fix acl2::x)
                                    acl2::y)
          (vl-elabinstruction-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: vl-elabinstruction-equiv-of-vl-elabinstruction-fix-2-forward

(defthm vl-elabinstruction-equiv-of-vl-elabinstruction-fix-2-forward
  (implies
       (vl-elabinstruction-equiv acl2::x
                                 (vl-elabinstruction-fix acl2::y))
       (vl-elabinstruction-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)