• 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
      • Sv-tutorial
      • Expressions
        • Rewriting
        • Svex
          • Svar
          • Least-fixpoint
          • Svex-p
          • Svex-select
            • Svex-select-staticify-assignment
            • Svex-select-fix
            • Svex-select-case
            • Svex-select-split-static
            • Svex-select-p
            • Svex-selects-merge
            • Svex-select-replace-indices
            • Svex-select-vars
            • Svex-select-to-svex-with-substitution
            • Svex-select-equiv
            • Svex-select-part
            • Svex-select-count
            • Svex-select-var
            • Svex-select-to-lhs
            • Svex-select-staticp
            • Svex-select-inner-var
            • Svex-select->indices
            • Svex-select-to-svex
            • Svex-select-inner-width
            • Svex-select->width
            • Svex-select-kind
          • 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

• Svex-select

Svex-select-equiv

Basic equivalence relation for svex-select structures.

Definitions and Theorems

Function: svex-select-equiv$inline

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

Theorem: svex-select-equiv-is-an-equivalence

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

Theorem: svex-select-equiv-implies-equal-svex-select-fix-1

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

Theorem: svex-select-fix-under-svex-select-equiv

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

Theorem: equal-of-svex-select-fix-1-forward-to-svex-select-equiv

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

Theorem: equal-of-svex-select-fix-2-forward-to-svex-select-equiv

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

Theorem: svex-select-equiv-of-svex-select-fix-1-forward

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

Theorem: svex-select-equiv-of-svex-select-fix-2-forward

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