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• Load-funct

Load-funct-equiv

Basic equivalence relation for load-funct structures.

Definitions and Theorems

Function: load-funct-equiv$inline

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

Theorem: load-funct-equiv-is-an-equivalence

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

Theorem: load-funct-equiv-implies-equal-load-funct-fix-1

(defthm load-funct-equiv-implies-equal-load-funct-fix-1
  (implies (load-funct-equiv acl2::x x-equiv)
           (equal (load-funct-fix acl2::x)
                  (load-funct-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: load-funct-fix-under-load-funct-equiv

(defthm load-funct-fix-under-load-funct-equiv
  (load-funct-equiv (load-funct-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-load-funct-fix-1-forward-to-load-funct-equiv

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

Theorem: equal-of-load-funct-fix-2-forward-to-load-funct-equiv

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

Theorem: load-funct-equiv-of-load-funct-fix-1-forward

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

Theorem: load-funct-equiv-of-load-funct-fix-2-forward

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