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• Tterm

Tterm-equiv

Basic equivalence relation for tterm structures.

Definitions and Theorems

Function: tterm-equiv$inline

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

Theorem: tterm-equiv-is-an-equivalence

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

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

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

Theorem: tterm-fix-under-tterm-equiv

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

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

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

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

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

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

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

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

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