		Search-engine friendly clone of the ACL2 documentation.

Map

This is similar to the fixtype set::set of osets.

Definitions and Theorems

Function: mequiv$inline

(defun mequiv$inline (acl2::x acl2::y)
       (declare (xargs :guard (and (mapp acl2::x) (mapp acl2::y))))
       (equal (mfix acl2::x) (mfix acl2::y)))

Theorem: mequiv-is-an-equivalence

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

Theorem: mequiv-implies-equal-mfix-1

(defthm mequiv-implies-equal-mfix-1
        (implies (mequiv acl2::x x-equiv)
                 (equal (mfix acl2::x) (mfix x-equiv)))
        :rule-classes (:congruence))

Theorem: mfix-under-mequiv

(defthm mfix-under-mequiv
        (mequiv (mfix acl2::x) acl2::x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-mfix-1-forward-to-mequiv

(defthm equal-of-mfix-1-forward-to-mequiv
        (implies (equal (mfix acl2::x) acl2::y)
                 (mequiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: equal-of-mfix-2-forward-to-mequiv

(defthm equal-of-mfix-2-forward-to-mequiv
        (implies (equal acl2::x (mfix acl2::y))
                 (mequiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: mequiv-of-mfix-1-forward

(defthm mequiv-of-mfix-1-forward
        (implies (mequiv (mfix acl2::x) acl2::y)
                 (mequiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: mequiv-of-mfix-2-forward

(defthm mequiv-of-mfix-2-forward
        (implies (mequiv acl2::x (mfix acl2::y))
                 (mequiv acl2::x acl2::y))
        :rule-classes :forward-chaining)