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• Objdesign-option

Objdesign-option-equiv

Basic equivalence relation for objdesign-option structures.

Definitions and Theorems

Function: objdesign-option-equiv$inline

(defun objdesign-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (objdesign-optionp acl2::x)
                              (objdesign-optionp acl2::y))))
  (equal (objdesign-option-fix acl2::x)
         (objdesign-option-fix acl2::y)))

Theorem: objdesign-option-equiv-is-an-equivalence

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

Theorem: objdesign-option-equiv-implies-equal-objdesign-option-fix-1

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

Theorem: objdesign-option-fix-under-objdesign-option-equiv

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

Theorem: equal-of-objdesign-option-fix-1-forward-to-objdesign-option-equiv

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

Theorem: equal-of-objdesign-option-fix-2-forward-to-objdesign-option-equiv

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

Theorem: objdesign-option-equiv-of-objdesign-option-fix-1-forward

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

Theorem: objdesign-option-equiv-of-objdesign-option-fix-2-forward

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