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• Output-section

Output-section-equiv

Basic equivalence relation for output-section structures.

Definitions and Theorems

Function: output-section-equiv$inline

(defun output-section-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (output-sectionp acl2::x)
                              (output-sectionp acl2::y))))
  (equal (output-section-fix acl2::x)
         (output-section-fix acl2::y)))

Theorem: output-section-equiv-is-an-equivalence

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

Theorem: output-section-equiv-implies-equal-output-section-fix-1

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

Theorem: output-section-fix-under-output-section-equiv

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

Theorem: equal-of-output-section-fix-1-forward-to-output-section-equiv

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

Theorem: equal-of-output-section-fix-2-forward-to-output-section-equiv

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

Theorem: output-section-equiv-of-output-section-fix-1-forward

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

Theorem: output-section-equiv-of-output-section-fix-2-forward

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