• 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
        • Address
        • Wire
        • Module
        • Lhs
          • Lhs.lisp
          • Lhs-p
          • Lhs-fix
          • Lhrange
            • Lhrange-fix
            • Lhrange-equiv
            • Lhrange-p
            • Make-lhrange
            • Lhrange-eval
            • Lhrange->atom
            • Lhrange->w
            • Change-lhrange
            • Lhrange->svex
          • Lhs-eval-zx
          • Lhs-equiv
          • Lhs-eval
          • Lhs->svex
        • Path
        • Svar-add-namespace
        • Design
        • Modinst
        • Lhs-add-namespace
        • Modalist
        • Path-add-namespace
        • Modname->submodnames
        • Name
        • Constraintlist-addr-p
        • Svex-alist-addr-p
        • Svar-map-addr-p
        • Lhspairs-addr-p
        • Modname
        • Assigns-addr-p
        • Lhs-addr-p
        • Lhatom-addr-p
        • Modhier-list-measure
        • Attributes
        • Modhier-measure
        • Modhier-list-measure-aux
        • Modhier-loopfreelist-p
        • Modhier-loopfree-p
      • Svstmt
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Vwsim
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Lhrange

Lhrange-equiv

Basic equivalence relation for lhrange structures.

Definitions and Theorems

Function: lhrange-equiv$inline

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

Theorem: lhrange-equiv-is-an-equivalence

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

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

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

Theorem: lhrange-fix-under-lhrange-equiv

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

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

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

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

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

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

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

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

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