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• Mach-o-section-headers

Mach-o-section-headers-equiv

Basic equivalence relation for mach-o-section-headers structures.

Definitions and Theorems

Function: mach-o-section-headers-equiv$inline

(defun mach-o-section-headers-equiv$inline (x y)
  (declare (xargs :guard (and (mach-o-section-headers-p x)
                              (mach-o-section-headers-p y))))
  (equal (mach-o-section-headers-fix x)
         (mach-o-section-headers-fix y)))

Theorem: mach-o-section-headers-equiv-is-an-equivalence

(defthm mach-o-section-headers-equiv-is-an-equivalence
  (and (booleanp (mach-o-section-headers-equiv x y))
       (mach-o-section-headers-equiv x x)
       (implies (mach-o-section-headers-equiv x y)
                (mach-o-section-headers-equiv y x))
       (implies (and (mach-o-section-headers-equiv x y)
                     (mach-o-section-headers-equiv y z))
                (mach-o-section-headers-equiv x z)))
  :rule-classes (:equivalence))

Theorem: mach-o-section-headers-equiv-implies-equal-mach-o-section-headers-fix-1

(defthm
 mach-o-section-headers-equiv-implies-equal-mach-o-section-headers-fix-1
 (implies (mach-o-section-headers-equiv x x-equiv)
          (equal (mach-o-section-headers-fix x)
                 (mach-o-section-headers-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: mach-o-section-headers-fix-under-mach-o-section-headers-equiv

(defthm
      mach-o-section-headers-fix-under-mach-o-section-headers-equiv
  (mach-o-section-headers-equiv (mach-o-section-headers-fix x)
                                x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-mach-o-section-headers-fix-1-forward-to-mach-o-section-headers-equiv

(defthm
 equal-of-mach-o-section-headers-fix-1-forward-to-mach-o-section-headers-equiv
 (implies (equal (mach-o-section-headers-fix x) y)
          (mach-o-section-headers-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-mach-o-section-headers-fix-2-forward-to-mach-o-section-headers-equiv

(defthm
 equal-of-mach-o-section-headers-fix-2-forward-to-mach-o-section-headers-equiv
 (implies (equal x (mach-o-section-headers-fix y))
          (mach-o-section-headers-equiv x y))
 :rule-classes :forward-chaining)

Theorem: mach-o-section-headers-equiv-of-mach-o-section-headers-fix-1-forward

(defthm
 mach-o-section-headers-equiv-of-mach-o-section-headers-fix-1-forward
 (implies
      (mach-o-section-headers-equiv (mach-o-section-headers-fix x)
                                    y)
      (mach-o-section-headers-equiv x y))
 :rule-classes :forward-chaining)

Theorem: mach-o-section-headers-equiv-of-mach-o-section-headers-fix-2-forward

(defthm
 mach-o-section-headers-equiv-of-mach-o-section-headers-fix-2-forward
 (implies
     (mach-o-section-headers-equiv x (mach-o-section-headers-fix y))
     (mach-o-section-headers-equiv x y))
 :rule-classes :forward-chaining)