• 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
        • Alias-normalization
        • Svex-design-flatten-and-normalize
        • Svex-design-compile
        • Svex-composition
        • Compile.lisp
          • Svex-normalize-assigns
          • Svex-design-flatten
          • Svex-override-lhrange
          • Svex-override-lhs
          • Aliases-indexed->named-aux
          • Svex-compose-assigns/delays
          • Svex-alist-truncate-by-var-decls
          • Svar-map-truncate-by-var-decls
          • Aliases-to-var-decl-map-aux
          • Aliases-indexed->named
          • Svar-indexed->named-memo
          • Lhs-indexed->named
          • Svar-register-indnamememo
          • Svarlist-indexed->named
          • Maybe-svar-fix
          • Lhs-register-indnamememo
          • Maybe-indname-result
          • Aliases-to-var-decl-map
          • Svar-indexed->named
          • Aliases-boundedp-aux
          • Svex-apply-overrides
          • Indnamememo-to-var-decl-map
          • Indname-result
          • Assigns-compose
          • Delay-svarlist->delays
          • Indnamememo
          • Svex-override-vars
          • Delay-svar->delays
          • Assigns-to-overrides
          • Svarlist-collect-delays
          • Svex-overridelist-vars
          • Svex-overridelist-keys
          • Assigns-to-overrides-nrev
          • Var-decl-map
            • Var-decl-map-p
            • Var-decl-map-fix
            • Var-decl-map-equiv
          • Cap-length
        • Assign->segment-drivers
        • Segment-driver-map-resolve
        • Assigns->segment-drivers
      • Moddb
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Vwsim
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Var-decl-map

Var-decl-map-equiv

Basic equivalence relation for var-decl-map structures.

Definitions and Theorems

Function: var-decl-map-equiv$inline

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

Theorem: var-decl-map-equiv-is-an-equivalence

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

Theorem: var-decl-map-equiv-implies-equal-var-decl-map-fix-1

(defthm var-decl-map-equiv-implies-equal-var-decl-map-fix-1
  (implies (var-decl-map-equiv x x-equiv)
           (equal (var-decl-map-fix x)
                  (var-decl-map-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: var-decl-map-fix-under-var-decl-map-equiv

(defthm var-decl-map-fix-under-var-decl-map-equiv
  (var-decl-map-equiv (var-decl-map-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-var-decl-map-fix-1-forward-to-var-decl-map-equiv

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

Theorem: equal-of-var-decl-map-fix-2-forward-to-var-decl-map-equiv

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

Theorem: var-decl-map-equiv-of-var-decl-map-fix-1-forward

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

Theorem: var-decl-map-equiv-of-var-decl-map-fix-2-forward

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