• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Fgl
      • Fgl-rewrite-rules
      • Fgl-function-mode
      • Fgl-object
      • Fgl-solving
      • Fgl-handling-if-then-elses
      • Fgl-getting-bits-from-objects
      • Fgl-primitive-and-meta-rules
      • Fgl-counterexamples
      • Fgl-interpreter-overview
      • Fgl-correctness-of-binding-free-variables
      • Fgl-debugging
      • Fgl-testbenches
      • Def-fgl-boolean-constraint
      • Fgl-stack
        • Scratchobj
        • Minor-frame
        • Major-frame
        • Major-stack
        • Scratchlist
        • Minor-stack
          • Minor-stack-fix
          • Minor-stack-equiv
          • Minor-stack-p
      • Fgl-rewrite-tracing
      • Def-fgl-param-thm
      • Def-fgl-thm
      • Fgl-fast-alist-support
      • Fgl-array-support
      • Advanced-equivalence-checking-with-fgl
      • Fgl-fty-support
      • Fgl-internals
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Minor-stack

Minor-stack-equiv

Basic equivalence relation for minor-stack structures.

Definitions and Theorems

Function: minor-stack-equiv$inline

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

Theorem: minor-stack-equiv-is-an-equivalence

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

Theorem: minor-stack-equiv-implies-equal-minor-stack-fix-1

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

Theorem: minor-stack-fix-under-minor-stack-equiv

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

Theorem: equal-of-minor-stack-fix-1-forward-to-minor-stack-equiv

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

Theorem: equal-of-minor-stack-fix-2-forward-to-minor-stack-equiv

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

Theorem: minor-stack-equiv-of-minor-stack-fix-1-forward

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

Theorem: minor-stack-equiv-of-minor-stack-fix-2-forward

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