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• Elf-header

Elf-header-equiv

Basic equivalence relation for elf-header structures.

Definitions and Theorems

Function: elf-header-equiv$inline

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

Theorem: elf-header-equiv-is-an-equivalence

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

Theorem: elf-header-equiv-implies-equal-elf-header-fix-1

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

Theorem: elf-header-fix-under-elf-header-equiv

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

Theorem: equal-of-elf-header-fix-1-forward-to-elf-header-equiv

(defthm equal-of-elf-header-fix-1-forward-to-elf-header-equiv
  (implies (equal (elf-header-fix x) y)
           (elf-header-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-elf-header-fix-2-forward-to-elf-header-equiv

(defthm equal-of-elf-header-fix-2-forward-to-elf-header-equiv
  (implies (equal x (elf-header-fix y))
           (elf-header-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf-header-equiv-of-elf-header-fix-1-forward

(defthm elf-header-equiv-of-elf-header-fix-1-forward
  (implies (elf-header-equiv (elf-header-fix x) y)
           (elf-header-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf-header-equiv-of-elf-header-fix-2-forward

(defthm elf-header-equiv-of-elf-header-fix-2-forward
  (implies (elf-header-equiv x (elf-header-fix y))
           (elf-header-equiv x y))
  :rule-classes :forward-chaining)