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• Tfunction

Tfunction-equiv

Basic equivalence relation for tfunction structures.

Definitions and Theorems

Function: tfunction-equiv$inline

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

Theorem: tfunction-equiv-is-an-equivalence

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

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

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

Theorem: tfunction-fix-under-tfunction-equiv

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

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

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

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

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

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

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

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

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