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Classname/params

Classname/params-equiv

Basic equivalence relation for classname/params structures.

Definitions and Theorems

Function: classname/params-equiv$inline

(defun classname/params-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (classname/params-p acl2::x)
                              (classname/params-p acl2::y))))
  (equal (classname/params-fix acl2::x)
         (classname/params-fix acl2::y)))

Theorem: classname/params-equiv-is-an-equivalence

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

Theorem: classname/params-equiv-implies-equal-classname/params-fix-1

(defthm classname/params-equiv-implies-equal-classname/params-fix-1
  (implies (classname/params-equiv acl2::x x-equiv)
           (equal (classname/params-fix acl2::x)
                  (classname/params-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: classname/params-fix-under-classname/params-equiv

(defthm classname/params-fix-under-classname/params-equiv
  (classname/params-equiv (classname/params-fix acl2::x)
                          acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-classname/params-fix-1-forward-to-classname/params-equiv

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

Theorem: equal-of-classname/params-fix-2-forward-to-classname/params-equiv

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

Theorem: classname/params-equiv-of-classname/params-fix-1-forward

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

Theorem: classname/params-equiv-of-classname/params-fix-2-forward

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