• 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-comb-transforms
          • Fraig
          • Parametrize
          • Observability-fix
          • Constprop
          • Apply-m-assumption-n-output-output-transform-default
          • Balance
          • Apply-n-output-comb-transform-default
          • Apply-comb-transform-default
          • Obs-constprop
          • Rewrite
          • Comb-transform
            • Fraig-config
            • Comb-transform-p
            • Comb-transform-fix
            • Rewrite-config
            • Obs-constprop-config
            • Observability-config
            • Constprop-config
            • Abc-comb-simp-config
            • M-assum-n-output-observability-config
            • Comb-transform-equiv
            • Snapshot-config
            • Prune-config
          • Abc-comb-simplify
          • Prune
          • Rewrite!
          • M-assumption-n-output-comb-transform->name
          • N-output-comb-transform->name
          • Comb-transform->name
          • N-output-comb-transformlist
          • M-assumption-n-output-comb-transformlist
          • Comb-transformlist
          • Apply-comb-transform
        • 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
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Comb-transform

Comb-transform-equiv

Basic equivalence relation for comb-transform structures.

Definitions and Theorems

Function: comb-transform-equiv$inline

(defun comb-transform-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (comb-transform-p x)
                              (comb-transform-p acl2::y))))
  (equal (comb-transform-fix x)
         (comb-transform-fix acl2::y)))

Theorem: comb-transform-equiv-is-an-equivalence

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

Theorem: comb-transform-equiv-implies-equal-comb-transform-fix-1

(defthm comb-transform-equiv-implies-equal-comb-transform-fix-1
  (implies (comb-transform-equiv x x-equiv)
           (equal (comb-transform-fix x)
                  (comb-transform-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: comb-transform-fix-under-comb-transform-equiv

(defthm comb-transform-fix-under-comb-transform-equiv
  (comb-transform-equiv (comb-transform-fix x)
                        x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-comb-transform-fix-1-forward-to-comb-transform-equiv

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

Theorem: equal-of-comb-transform-fix-2-forward-to-comb-transform-equiv

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

Theorem: comb-transform-equiv-of-comb-transform-fix-1-forward

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

Theorem: comb-transform-equiv-of-comb-transform-fix-2-forward

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