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• Values+denv-result

Values+denv-result-equiv

Basic equivalence relation for values+denv-result structures.

Definitions and Theorems

Function: values+denv-result-equiv$inline

(defun values+denv-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (values+denv-resultp acl2::x)
                              (values+denv-resultp acl2::y))))
  (equal (values+denv-result-fix acl2::x)
         (values+denv-result-fix acl2::y)))

Theorem: values+denv-result-equiv-is-an-equivalence

(defthm values+denv-result-equiv-is-an-equivalence
  (and (booleanp (values+denv-result-equiv x y))
       (values+denv-result-equiv x x)
       (implies (values+denv-result-equiv x y)
                (values+denv-result-equiv y x))
       (implies (and (values+denv-result-equiv x y)
                     (values+denv-result-equiv y z))
                (values+denv-result-equiv x z)))
  :rule-classes (:equivalence))

Theorem: values+denv-result-equiv-implies-equal-values+denv-result-fix-1

(defthm
    values+denv-result-equiv-implies-equal-values+denv-result-fix-1
  (implies (values+denv-result-equiv acl2::x x-equiv)
           (equal (values+denv-result-fix acl2::x)
                  (values+denv-result-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: values+denv-result-fix-under-values+denv-result-equiv

(defthm values+denv-result-fix-under-values+denv-result-equiv
  (values+denv-result-equiv (values+denv-result-fix acl2::x)
                            acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-values+denv-result-fix-1-forward-to-values+denv-result-equiv

(defthm
 equal-of-values+denv-result-fix-1-forward-to-values+denv-result-equiv
 (implies (equal (values+denv-result-fix acl2::x)
                 acl2::y)
          (values+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-values+denv-result-fix-2-forward-to-values+denv-result-equiv

(defthm
 equal-of-values+denv-result-fix-2-forward-to-values+denv-result-equiv
 (implies (equal acl2::x
                 (values+denv-result-fix acl2::y))
          (values+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: values+denv-result-equiv-of-values+denv-result-fix-1-forward

(defthm values+denv-result-equiv-of-values+denv-result-fix-1-forward
 (implies (values+denv-result-equiv (values+denv-result-fix acl2::x)
                                    acl2::y)
          (values+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: values+denv-result-equiv-of-values+denv-result-fix-2-forward

(defthm values+denv-result-equiv-of-values+denv-result-fix-2-forward
  (implies
       (values+denv-result-equiv acl2::x
                                 (values+denv-result-fix acl2::y))
       (values+denv-result-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)