• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • 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-constraints
        • Svstmt-jump
        • Svstmtlist
          • Svstmtlist-equiv
          • Svstmtlist-p
          • Svstmtlist-fix
        • Svstmt-kind
        • Svstmt.lisp
        • Svstmt-fix
        • Svstmt-count
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Svstmtlist

Svstmtlist-equiv

Basic equivalence relation for svstmtlist structures.

Definitions and Theorems

Function: svstmtlist-equiv$inline

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

Theorem: svstmtlist-equiv-is-an-equivalence

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

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

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

Theorem: svstmtlist-fix-under-svstmtlist-equiv

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

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

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

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

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

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

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

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

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