• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
      • Index-permute-shrink
      • Permute-stretch
      • Env-mismatch-aux
      • Permute-shrink
      • Permute-polarity
      • Env-permute-polarity
      • Env-permute-shrink
      • Permute-var-down
      • Swap-vars-aux
      • Env-permute-stretch
      • Swap-vars
      • Permute-var-up
      • Negative-cofactor
      • Truth-perm-rev
      • Index-permute-stretch
      • Env-mismatch
      • Truth-perm
      • Swap-polarity
      • Positive-cofactor
      • Index-perm-rev
      • Env-perm-rev
      • Nth-set-bit-pos
      • Index-swap
      • Env-move-var-down
      • Is-xor-with-var
      • Index-perm
      • Env-swap-vars
      • Var
      • Truth-eval
      • Index-move-down
      • Env-update
      • Env-perm
      • Depends-on-witness
      • Env-swap-polarity
      • Var-repetitions
      • Env-move-var-up
      • Index-move-up
      • Depends-on
      • Truth-norm
      • Index-listp
      • Env-diff-index
      • Env-lookup
      • True
      • False
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Testing-utilities
  • Math

• Truth

Index-permute-stretch

Signature

(index-permute-stretch n count mask x numvars) → perm-index

Arguments

n — Guard (natp n).

mask — Guard (natp mask).

x — Guard (natp x).

numvars — Guard (natp numvars).

Returns

perm-index — Type (natp perm-index).

Definitions and Theorems

Function: index-permute-stretch

(defun
  index-permute-stretch
  (n count mask x numvars)
  (declare (xargs :guard (and (natp n)
                              (natp mask)
                              (natp x)
                              (natp numvars))))
  (declare
       (xargs :guard (and (<= n numvars)
                          (eql count (logcount (loghead n mask))))))
  (let ((__function__ 'index-permute-stretch))
       (declare (ignorable __function__))
       (b* (((when (mbe :logic (zp (- (nfix numvars) (nfix n)))
                        :exec (eql n numvars)))
             (lnfix x))
            (n (lnfix n))
            (count (mbe :logic (logcount (loghead n (lnfix mask)))
                        :exec count))
            (bit (logbit n (lnfix mask)))
            (x (index-permute-stretch (1+ n)
                                      (+ bit count)
                                      mask x numvars)))
           (if (eql bit 1)
               (index-move-up count n x)
               x))))

Theorem: natp-of-index-permute-stretch

(defthm
   natp-of-index-permute-stretch
   (b* ((perm-index (index-permute-stretch n count mask x numvars)))
       (natp perm-index))
   :rule-classes :type-prescription)

Theorem: index-permute-stretch-bound

(defthm
  index-permute-stretch-bound
  (b* ((?perm-index (index-permute-stretch n count mask x numvars)))
      (implies (< (nfix x) (nfix numvars))
               (< perm-index (nfix numvars))))
  :rule-classes :linear)

Theorem: index-permute-stretch-normalize-count

(defthm
     index-permute-stretch-normalize-count
     (implies (syntaxp (not (equal count ''nil)))
              (equal (index-permute-stretch n count mask x numvars)
                     (index-permute-stretch n nil mask x numvars))))

Theorem: index-permute-stretch-of-nfix-n

(defthm index-permute-stretch-of-nfix-n
        (equal (index-permute-stretch (nfix n)
                                      count mask x numvars)
               (index-permute-stretch n count mask x numvars)))

Theorem: index-permute-stretch-nat-equiv-congruence-on-n

(defthm
  index-permute-stretch-nat-equiv-congruence-on-n
  (implies
       (nat-equiv n n-equiv)
       (equal (index-permute-stretch n count mask x numvars)
              (index-permute-stretch n-equiv count mask x numvars)))
  :rule-classes :congruence)

Theorem: index-permute-stretch-of-nfix-mask

(defthm index-permute-stretch-of-nfix-mask
        (equal (index-permute-stretch n count (nfix mask)
                                      x numvars)
               (index-permute-stretch n count mask x numvars)))

Theorem: index-permute-stretch-nat-equiv-congruence-on-mask

(defthm
  index-permute-stretch-nat-equiv-congruence-on-mask
  (implies
       (nat-equiv mask mask-equiv)
       (equal (index-permute-stretch n count mask x numvars)
              (index-permute-stretch n count mask-equiv x numvars)))
  :rule-classes :congruence)

Theorem: index-permute-stretch-of-nfix-x

(defthm index-permute-stretch-of-nfix-x
        (equal (index-permute-stretch n count mask (nfix x)
                                      numvars)
               (index-permute-stretch n count mask x numvars)))

Theorem: index-permute-stretch-nat-equiv-congruence-on-x

(defthm
  index-permute-stretch-nat-equiv-congruence-on-x
  (implies
       (nat-equiv x x-equiv)
       (equal (index-permute-stretch n count mask x numvars)
              (index-permute-stretch n count mask x-equiv numvars)))
  :rule-classes :congruence)

Theorem: index-permute-stretch-of-nfix-numvars

(defthm index-permute-stretch-of-nfix-numvars
        (equal (index-permute-stretch n count mask x (nfix numvars))
               (index-permute-stretch n count mask x numvars)))

Theorem: index-permute-stretch-nat-equiv-congruence-on-numvars

(defthm
  index-permute-stretch-nat-equiv-congruence-on-numvars
  (implies
       (nat-equiv numvars numvars-equiv)
       (equal (index-permute-stretch n count mask x numvars)
              (index-permute-stretch n count mask x numvars-equiv)))
  :rule-classes :congruence)