• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Svex-compilation
      • Moddb
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
        • Rewriting
        • Svex
          • Svar
            • Svar-p
            • Svar-fix
            • Make-svar
            • Svar-equiv
            • Svar->props
            • Svar->delay
            • Svar->bits
            • Change-svar
            • Svarlist
              • Svarlist-p
              • Svarlist-fix
              • Svarlist-equiv
            • Svar->name
            • Svar-map
            • Svar-alist
          • Least-fixpoint
          • Svex-p
          • Svex-select
          • Svex-alist
          • Svex-equiv
          • Svexlist
          • Svex-call
          • Fnsym
          • Svex-quote
          • Svex-var
          • Svcall-rw
          • Svcall
          • Svex-kind
          • Svcall*
          • Svex-fix
          • Svex-count
          • Svex-1z
          • Svex-1x
          • Svex-z
          • Svex-x
        • Bit-blasting
        • Functions
        • 4vmask
        • Why-infinite-width
        • Svex-vars
        • Evaluation
        • Values
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Svarlist

Svarlist-equiv

Basic equivalence relation for svarlist structures.

Definitions and Theorems

Function: svarlist-equiv$inline

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

Theorem: svarlist-equiv-is-an-equivalence

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

Theorem: svarlist-equiv-implies-equal-svarlist-fix-1

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

Theorem: svarlist-fix-under-svarlist-equiv

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

Theorem: equal-of-svarlist-fix-1-forward-to-svarlist-equiv

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

Theorem: equal-of-svarlist-fix-2-forward-to-svarlist-equiv

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

Theorem: svarlist-equiv-of-svarlist-fix-1-forward

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

Theorem: svarlist-equiv-of-svarlist-fix-2-forward

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