• 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

• Omaps

Rlookup*

Set of keys to which any value in a set is associated.

Signature

(rlookup* vals map) → keys

Arguments

vals — Guard (setp vals).

map — Guard (mapp map).

Returns

keys — Type (setp keys).

This lifts rlookup* to sets of values.

Definitions and Theorems

Function: rlookup*

(defun rlookup* (vals map)
  (declare (xargs :guard (and (setp vals) (mapp map))))
  (let ((__function__ 'rlookup*))
    (declare (ignorable __function__))
    (cond ((set::emptyp vals) nil)
          (t (union (rlookup (set::head vals) map)
                    (rlookup* (set::tail vals) map))))))

Theorem: setp-of-rlookup*

(defthm setp-of-rlookup*
  (b* ((keys (rlookup* vals map)))
    (setp keys))
  :rule-classes :rewrite)

Theorem: rlookup*-when-left-emptyp

(defthm rlookup*-when-left-emptyp
  (implies (set::emptyp vals)
           (equal (rlookup* vals map) nil))
  :rule-classes (:rewrite :type-prescription))

Theorem: rlookup*-when-right-emptyp

(defthm rlookup*-when-right-emptyp
  (implies (emptyp map)
           (equal (rlookup* vals map) nil))
  :rule-classes (:rewrite :type-prescription))