• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • 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
        • Svstmt-case
        • Svstmt-while
        • Svstmt-p
        • Svstmt-if
        • Svstmt-equiv
        • Svstmt-xcond
        • Svstmt-scope
        • Svstmt-assign
        • Svstmt-compile
          • Svstmt-compile.lisp
          • Svstate
            • Svstate-p
            • Svstate-fix
            • Svstate-equiv
            • Make-svstate
            • Svstate->nonblkst
            • Svstate->blkst
            • Change-svstate
        • Svstmt-constraints
        • Svstmt-jump
        • Svstmtlist
        • Svstmt-kind
        • Svstmt.lisp
        • Svstmt-fix
        • Svstmt-count
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Vwsim
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Svstate

Svstate-equiv

Basic equivalence relation for svstate structures.

Definitions and Theorems

Function: svstate-equiv$inline

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

Theorem: svstate-equiv-is-an-equivalence

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

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

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

Theorem: svstate-fix-under-svstate-equiv

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

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

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

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

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

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

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

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

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