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• Funinfo

Funinfo-equiv

Basic equivalence relation for funinfo structures.

Definitions and Theorems

Function: funinfo-equiv$inline

(defun funinfo-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (funinfop acl2::x)
                              (funinfop acl2::y))))
  (equal (funinfo-fix acl2::x)
         (funinfo-fix acl2::y)))

Theorem: funinfo-equiv-is-an-equivalence

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

Theorem: funinfo-equiv-implies-equal-funinfo-fix-1

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

Theorem: funinfo-fix-under-funinfo-equiv

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

Theorem: equal-of-funinfo-fix-1-forward-to-funinfo-equiv

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

Theorem: equal-of-funinfo-fix-2-forward-to-funinfo-equiv

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

Theorem: funinfo-equiv-of-funinfo-fix-1-forward

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

Theorem: funinfo-equiv-of-funinfo-fix-2-forward

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