• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
    • Std/osets
      • Omaps
        • Defomap
        • Update
        • Mapp
        • Assoc
        • Update*
        • Size
        • Keys
        • From-lists
        • Update-induction-on-maps
        • Compatiblep
        • Tail
        • Head
        • Restrict
        • Submap
        • Map
        • Rlookup
        • Emptyp
        • Rlookup*
        • Lookup*
        • Delete*
        • Values
        • In*
        • Lookup
        • Delete
        • Mfix
        • Head-val
        • Head-key
        • Omap-induction2
        • Omap-order-rules
      • All-by-membership
      • Defset
      • In
      • Primitives
      • Subset
      • Mergesort
      • Intersect
      • Union
      • Pick-a-point-subset-strategy
      • Delete
      • Double-containment
      • Difference
      • Cardinality
      • Set
      • Intersectp
    • Std/io
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Fty-extensions
• Specific-types
• Omaps

Map

A fixtype of omaps.

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)