• 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-vars-normorderedp
            • Lhs-norm
            • Lhatom-normorderedp
            • Lhs-normp
            • Svex-lhsrewrite-aux
            • Lhs-concat
            • Lhs-check-masks
            • Lhrange-combine
            • Svexarr-vars-aux
            • Assigns-check-masks
            • Svex->lhs-range
            • Svex-lhs-preproc-blkrev
            • Svarlist-boundedp-badguy
            • Driverlist-rest-after-strength
            • Aliases-normorderedp
            • Lhs-rsh
            • Lhs-cons
            • Svarlist-boundedp
            • Lhs-bitproj
            • Lhs-vars
            • Driver
            • Svex-override
            • Make-simple-lhs
            • Lhssvex-range-p
            • Lhs-override
            • Lhs-first-aux
            • Lhrange-combinable-dec
            • Lhrange-bitproj
            • Lhatom
            • Driverlist-values-of-strength
            • Lhs-rest-aux
            • Lhs-rest
            • Aliases-normorderedp-aux
            • Svexarr-vars
            • Lhsarr-to-svexarr
            • Svexarr-vars-witness-aux
            • Lhbit
            • Svex-lhsrewrite
            • Svar-boundedp
            • Lhs-decomp-aux
            • Svex->lhs-bound
            • Aliases-vars-aux
            • Svexarr
            • Svexarr-vars-witness
            • Svar-set-index
            • Lhsarr
            • Lhs-override-vars
            • Lhatom-eval-zero
            • Lhatom-bitproj
            • Lhrange-nextbit
            • Lhrange-combinable
            • Driverlist->svex
            • Svexlist-resolve
            • Lhs->svex-zero
            • Lhs-overridelist-vars
            • Lhs-overridelist-keys
            • Lhbit-eval
            • Driverlist-vars
            • Assigns-vars
            • Svex-int
            • Lhssvex-bounded-p
            • Lhslist-vars
            • Lhs-decomp
            • Lhatom-vars
            • Svar-map-vars
            • Lhssvex-unbounded-p
            • Lhspairs-vars
            • Lhs-width
            • Aliases-vars
            • Lhs-first
            • Svar-index
            • Assigns
            • Svar-indexedp
            • Lhspairs
            • Svex-overridelist
            • Lhslist
            • Lhs-overridelist
            • Driverlist
            • Svex-lhs-preproc
            • Svexarr-fix
            • Lhsarr-fix
          • Lhs-p
          • Lhs-fix
          • Lhrange
          • 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

• Lhs.lisp

Lhs-vars-normorderedp

Signature

(lhs-vars-normorderedp bound offset x) → *

Arguments

bound — Guard (integerp bound).

offset — Guard (natp offset).

x — Guard (lhs-p x).

Definitions and Theorems

Function: lhs-vars-normorderedp

(defun lhs-vars-normorderedp (bound offset x)
 (declare (xargs :guard (and (integerp bound)
                             (natp offset)
                             (lhs-p x))))
 (let ((__function__ 'lhs-vars-normorderedp))
  (declare (ignorable __function__))
  (if (atom x)
      t
   (and
      (lhatom-normorderedp bound offset (lhrange->atom (car x)))
      (lhs-vars-normorderedp bound
                             (+ (lhrange->w (car x)) (lnfix offset))
                             (cdr x))))))

Theorem: lhs-vars-normorderedp-of-ifix-bound

(defthm lhs-vars-normorderedp-of-ifix-bound
  (equal (lhs-vars-normorderedp (ifix bound)
                                offset x)
         (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-int-equiv-congruence-on-bound

(defthm lhs-vars-normorderedp-int-equiv-congruence-on-bound
  (implies (int-equiv bound bound-equiv)
           (equal (lhs-vars-normorderedp bound offset x)
                  (lhs-vars-normorderedp bound-equiv offset x)))
  :rule-classes :congruence)

Theorem: lhs-vars-normorderedp-of-nfix-offset

(defthm lhs-vars-normorderedp-of-nfix-offset
  (equal (lhs-vars-normorderedp bound (nfix offset)
                                x)
         (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-nat-equiv-congruence-on-offset

(defthm lhs-vars-normorderedp-nat-equiv-congruence-on-offset
  (implies (nat-equiv offset offset-equiv)
           (equal (lhs-vars-normorderedp bound offset x)
                  (lhs-vars-normorderedp bound offset-equiv x)))
  :rule-classes :congruence)

Theorem: lhs-vars-normorderedp-of-lhs-fix-x

(defthm lhs-vars-normorderedp-of-lhs-fix-x
  (equal (lhs-vars-normorderedp bound offset (lhs-fix x))
         (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-lhs-equiv-congruence-on-x

(defthm lhs-vars-normorderedp-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-vars-normorderedp bound offset x)
                  (lhs-vars-normorderedp bound offset x-equiv)))
  :rule-classes :congruence)

Theorem: lhs-vars-normorderedp-of-lhs-cons

(defthm lhs-vars-normorderedp-of-lhs-cons
  (equal (lhs-vars-normorderedp bound offset (lhs-cons x y))
         (lhs-vars-normorderedp bound offset (cons x y))))

Theorem: lhs-vars-normorderedp-of-lhs-norm-x

(defthm lhs-vars-normorderedp-of-lhs-norm-x
  (equal (lhs-vars-normorderedp bound offset (lhs-norm x))
         (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-lhs-norm-equiv-congruence-on-x

(defthm lhs-vars-normorderedp-lhs-norm-equiv-congruence-on-x
  (implies (lhs-norm-equiv x x-equiv)
           (equal (lhs-vars-normorderedp bound offset x)
                  (lhs-vars-normorderedp bound offset x-equiv)))
  :rule-classes :congruence)

Theorem: lhs-vars-normorderedp-implies-rest

(defthm lhs-vars-normorderedp-implies-rest
  (implies (and (lhs-vars-normorderedp bound offset x)
                (equal (nfix offset1)
                       (+ (nfix offset) (lhrange->w (car x)))))
           (lhs-vars-normorderedp bound offset1 (cdr x))))

Theorem: lhs-vars-normorderedp-implies-rest-strict

(defthm lhs-vars-normorderedp-implies-rest-strict
 (implies
  (and (<= (lhrange->w (car x)) (nfix offset))
       (lhs-vars-normorderedp bound
                              (- (nfix offset) (lhrange->w (car x)))
                              x))
  (lhs-vars-normorderedp bound offset (cdr x))))

Theorem: lhs-vars-normorderedp-implies-atom-normorderedp-of-car

(defthm lhs-vars-normorderedp-implies-atom-normorderedp-of-car
  (implies
       (and (lhs-vars-normorderedp bound offset x)
            (consp x))
       (lhatom-normorderedp bound offset (lhrange->atom (car x)))))

Theorem: lhs-vars-normorderedp-implies-index-bound

(defthm lhs-vars-normorderedp-implies-index-bound
  (implies
       (and (lhs-vars-normorderedp bound offset x)
            (consp x)
            (eq (lhatom-kind (lhrange->atom (car x)))
                :var))
       (<= (svar-index (lhatom-var->name (lhrange->atom (car x))))
           (ifix bound)))
  :rule-classes :linear)

Theorem: lhs-vars-normorderedp-implies-rsh-when-index-equal

(defthm lhs-vars-normorderedp-implies-rsh-when-index-equal
 (implies
  (and
      (lhs-vars-normorderedp bound offset x)
      (consp x)
      (eq (lhatom-kind (lhrange->atom (car x)))
          :var)
      (equal (svar-index (lhatom-var->name (lhrange->atom (car x))))
             (ifix bound)))
  (<= (lhatom-var->rsh (lhrange->atom (car x)))
      (nfix offset)))
 :rule-classes :linear)

Theorem: lhs-vars-normorderedp-implies-lhs-bitproj-index

(defthm lhs-vars-normorderedp-implies-lhs-bitproj-index
  (implies (and (lhs-vars-normorderedp bound offset x)
                (eq (lhbit-kind (lhs-bitproj idx x))
                    :var))
           (svar-index (lhbit-var->name (lhs-bitproj idx x)))))

Theorem: lhs-vars-normorderedp-implies-lhs-bitproj-index-bound

(defthm lhs-vars-normorderedp-implies-lhs-bitproj-index-bound
  (implies (and (lhs-vars-normorderedp bound offset x)
                (eq (lhbit-kind (lhs-bitproj idx x))
                    :var))
           (<= (svar-index (lhbit-var->name (lhs-bitproj idx x)))
               (ifix bound)))
  :rule-classes :linear)

Theorem: lhs-vars-normorderedp-implies-lhs-bitproj-idx-when-index-bound

(defthm
     lhs-vars-normorderedp-implies-lhs-bitproj-idx-when-index-bound
 (implies
      (and (lhs-vars-normorderedp bound offset x)
           (eq (lhbit-kind (lhs-bitproj idx x))
               :var)
           (equal (svar-index (lhbit-var->name (lhs-bitproj idx x)))
                  (ifix bound)))
      (<= (lhbit-var->idx (lhs-bitproj idx x))
          (+ (nfix idx) (nfix offset))))
 :rule-classes :linear)

Theorem: lhs-vars-normorderedp-of-greater

(defthm lhs-vars-normorderedp-of-greater
  (implies (and (lhs-vars-normorderedp bound1 offset1 x)
                (<= (ifix bound1) (ifix bound))
                (<= (nfix offset1) (nfix offset)))
           (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-of-greater-bound

(defthm lhs-vars-normorderedp-of-greater-bound
  (implies (and (lhs-vars-normorderedp bound1 offset1 x)
                (< (ifix bound1) (ifix bound)))
           (lhs-vars-normorderedp bound offset x)))

Theorem: lhs-vars-normorderedp-of-rsh

(defthm lhs-vars-normorderedp-of-rsh
  (implies (and (lhs-vars-normorderedp bound offset x)
                (<= (+ (nfix offset) (nfix sh))
                    (nfix offset1)))
           (lhs-vars-normorderedp bound offset1 (lhs-rsh sh x))))

Theorem: lhs-vars-normorderedp-of-rsh-strict

(defthm lhs-vars-normorderedp-of-rsh-strict
  (implies (and (<= (nfix sh) (nfix offset1))
                (equal offset (- (nfix offset1) (nfix sh)))
                (lhs-vars-normorderedp bound offset x))
           (lhs-vars-normorderedp bound offset1 (lhs-rsh sh x))))

Theorem: lhs-vars-normorderedp-of-rsh-greater-bound

(defthm lhs-vars-normorderedp-of-rsh-greater-bound
  (implies (and (lhs-vars-normorderedp bound offset x)
                (< (ifix bound) (ifix bound1)))
           (lhs-vars-normorderedp bound1 offset1 (lhs-rsh sh x))))

Theorem: lhs-vars-normorderedp-of-concat-strict

(defthm lhs-vars-normorderedp-of-concat-strict
  (implies
       (and (lhs-vars-normorderedp bound offset x1)
            (lhs-vars-normorderedp bound (+ (nfix offset) (nfix w))
                                   x2))
       (lhs-vars-normorderedp bound offset (lhs-concat w x1 x2))))

Theorem: lhs-vars-normorderedp-of-concat

(defthm lhs-vars-normorderedp-of-concat
  (implies
       (and (lhs-vars-normorderedp bound offset x1)
            (lhs-vars-normorderedp bound offset2 x2)
            (<= (nfix offset2)
                (+ (nfix offset) (nfix w))))
       (lhs-vars-normorderedp bound offset (lhs-concat w x1 x2))))

Theorem: lhs-vars-normorderedp-implies-svarlist-boundedp

(defthm lhs-vars-normorderedp-implies-svarlist-boundedp
  (implies (lhs-vars-normorderedp bound offset x)
           (svarlist-boundedp (lhs-vars x)
                              (+ 1 (ifix bound)))))