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• Fundecl

Fundecl-equiv

Basic equivalence relation for fundecl structures.

Definitions and Theorems

Function: fundecl-equiv$inline

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

Theorem: fundecl-equiv-is-an-equivalence

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

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

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

Theorem: fundecl-fix-under-fundecl-equiv

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

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

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

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

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

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

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

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

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