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• Truth

Permute-var-up

Signature

(permute-var-up m n truth numvars) → perm-truth

Arguments

m — Guard (natp m).

n — Guard (natp n).

truth — Guard (integerp truth).

numvars — Guard (natp numvars).

Returns

perm-truth — Type (natp perm-truth).

Definitions and Theorems

Function: permute-var-up

(defun permute-var-up (m n truth numvars)
  (declare (xargs :guard (and (natp m)
                              (natp n)
                              (integerp truth)
                              (natp numvars))))
  (declare (xargs :guard (and (<= m n) (< n numvars))))
  (let ((__function__ 'permute-var-up))
    (declare (ignorable __function__))
    (b* (((when (mbe :logic (zp (- (nfix n) (nfix m)))
                     :exec (eql n m)))
          (truth-norm truth numvars))
         (next (1+ (lnfix m)))
         (truth (swap-vars next m truth numvars)))
      (permute-var-up next n truth numvars))))

Theorem: natp-of-permute-var-up

(defthm natp-of-permute-var-up
  (b* ((perm-truth (permute-var-up m n truth numvars)))
    (natp perm-truth))
  :rule-classes :type-prescription)

Theorem: eval-of-permute-var-up-with-env-move-var-up

(defthm eval-of-permute-var-up-with-env-move-var-up
  (b* ((?perm-truth (permute-var-up m n truth numvars)))
    (implies (and (<= (nfix m) (nfix n))
                  (< (nfix n) (nfix numvars)))
             (equal (truth-eval perm-truth (env-move-var-up m n env)
                                numvars)
                    (truth-eval truth env numvars)))))

Theorem: eval-of-permute-var-up

(defthm eval-of-permute-var-up
  (b* ((?perm-truth (permute-var-up m n truth numvars)))
    (implies (and (<= (nfix m) (nfix n))
                  (< (nfix n) (nfix numvars)))
             (equal (truth-eval perm-truth env numvars)
                    (truth-eval truth (env-move-var-down m n env)
                                numvars)))))

Theorem: size-of-permute-var-up

(defthm size-of-permute-var-up
  (b* ((?perm-truth (permute-var-up m n truth numvars)))
    (implies (and (< (nfix n) (nfix numvars))
                  (natp size)
                  (<= (ash 1 numvars) size))
             (unsigned-byte-p size perm-truth))))

Theorem: permute-var-up-of-truth-norm

(defthm permute-var-up-of-truth-norm
  (equal (permute-var-up m n (truth-norm truth numvars)
                         numvars)
         (permute-var-up m n truth numvars)))

Theorem: permute-var-up-of-nfix-m

(defthm permute-var-up-of-nfix-m
  (equal (permute-var-up (nfix m)
                         n truth numvars)
         (permute-var-up m n truth numvars)))

Theorem: permute-var-up-nat-equiv-congruence-on-m

(defthm permute-var-up-nat-equiv-congruence-on-m
  (implies (nat-equiv m m-equiv)
           (equal (permute-var-up m n truth numvars)
                  (permute-var-up m-equiv n truth numvars)))
  :rule-classes :congruence)

Theorem: permute-var-up-of-nfix-n

(defthm permute-var-up-of-nfix-n
  (equal (permute-var-up m (nfix n)
                         truth numvars)
         (permute-var-up m n truth numvars)))

Theorem: permute-var-up-nat-equiv-congruence-on-n

(defthm permute-var-up-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (permute-var-up m n truth numvars)
                  (permute-var-up m n-equiv truth numvars)))
  :rule-classes :congruence)

Theorem: permute-var-up-of-ifix-truth

(defthm permute-var-up-of-ifix-truth
  (equal (permute-var-up m n (ifix truth)
                         numvars)
         (permute-var-up m n truth numvars)))

Theorem: permute-var-up-int-equiv-congruence-on-truth

(defthm permute-var-up-int-equiv-congruence-on-truth
  (implies (int-equiv truth truth-equiv)
           (equal (permute-var-up m n truth numvars)
                  (permute-var-up m n truth-equiv numvars)))
  :rule-classes :congruence)

Theorem: permute-var-up-of-nfix-numvars

(defthm permute-var-up-of-nfix-numvars
  (equal (permute-var-up m n truth (nfix numvars))
         (permute-var-up m n truth numvars)))

Theorem: permute-var-up-nat-equiv-congruence-on-numvars

(defthm permute-var-up-nat-equiv-congruence-on-numvars
  (implies (nat-equiv numvars numvars-equiv)
           (equal (permute-var-up m n truth numvars)
                  (permute-var-up m n truth numvars-equiv)))
  :rule-classes :congruence)