• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
      • Base-api
      • Aignet-construction
      • Representation
      • Aignet-copy-init
      • Aignet-simplify-with-tracking
      • Aignet-simplify-marked-with-tracking
      • Aignet-cnf
      • Aignet-simplify-marked
      • Aignet-complete-copy
      • Aignet-transforms
        • Aignet-output-ranges
          • Aignet-output-range-map
            • Aignet-output-range-map-p
            • Aignet-output-range-map-fix
            • Aignet-output-range-map-equiv
        • Aignet-comb-transforms
        • Aignet-m-assumption-n-output-transforms
        • Aignet-n-output-comb-transforms
      • Aignet-eval
      • Semantics
      • Aignet-read-aiger
      • Aignet-write-aiger
      • Aignet-abc-interface
      • Utilities
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Aignet-output-range-map

Aignet-output-range-map-equiv

Basic equivalence relation for aignet-output-range-map structures.

Definitions and Theorems

Function: aignet-output-range-map-equiv$inline

(defun aignet-output-range-map-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (aignet-output-range-map-p x)
                              (aignet-output-range-map-p acl2::y))))
  (equal (aignet-output-range-map-fix x)
         (aignet-output-range-map-fix acl2::y)))

Theorem: aignet-output-range-map-equiv-is-an-equivalence

(defthm aignet-output-range-map-equiv-is-an-equivalence
  (and (booleanp (aignet-output-range-map-equiv x y))
       (aignet-output-range-map-equiv x x)
       (implies (aignet-output-range-map-equiv x y)
                (aignet-output-range-map-equiv y x))
       (implies (and (aignet-output-range-map-equiv x y)
                     (aignet-output-range-map-equiv y z))
                (aignet-output-range-map-equiv x z)))
  :rule-classes (:equivalence))

Theorem: aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1

(defthm
 aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1
 (implies (aignet-output-range-map-equiv x x-equiv)
          (equal (aignet-output-range-map-fix x)
                 (aignet-output-range-map-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: aignet-output-range-map-fix-under-aignet-output-range-map-equiv

(defthm
    aignet-output-range-map-fix-under-aignet-output-range-map-equiv
  (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                 x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv
 (implies (equal (aignet-output-range-map-fix x)
                 acl2::y)
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv
 (implies (equal x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward
 (implies
      (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                     acl2::y)
      (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward
 (implies (aignet-output-range-map-equiv
               x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)