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Jmethod

Jmethod-equiv

Basic equivalence relation for jmethod structures.

Definitions and Theorems

Function: jmethod-equiv$inline

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

Theorem: jmethod-equiv-is-an-equivalence

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

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

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

Theorem: jmethod-fix-under-jmethod-equiv

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

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

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

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

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

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

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

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

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