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Aliases-boundedp-aux

Signature

(aliases-boundedp-aux n aliases bound) → *

Arguments

n — Guard (natp n).

bound — Guard (natp bound).

Definitions and Theorems

Function: aliases-boundedp-aux

(defun aliases-boundedp-aux (n aliases bound)
 (declare (xargs :stobjs (aliases)))
 (declare (xargs :guard (and (natp n) (natp bound))))
 (declare (xargs :guard (<= (lnfix n) (aliass-length aliases))))
 (let ((__function__ 'aliases-boundedp-aux))
   (declare (ignorable __function__))
   (b* (((when (mbe :logic (zp (- (aliass-length aliases) (nfix n)))
                    :exec (eql (aliass-length aliases) n)))
         t))
     (and (svarlist-boundedp (lhs-vars (get-alias n aliases))
                             bound)
          (aliases-boundedp-aux (1+ (lnfix n))
                                aliases bound)))))

Theorem: aliases-boundedp-aux-of-update-less

(defthm aliases-boundedp-aux-of-update-less
  (implies (< (nfix m) (nfix n))
           (equal (aliases-boundedp-aux n (update-nth m val aliases)
                                        bound)
                  (aliases-boundedp-aux n aliases bound))))

Theorem: aliases-boundedp-aux-when-normordered

(defthm aliases-boundedp-aux-when-normordered
  (implies (and (aliases-normorderedp aliases)
                (<= (len aliases) (nfix bound)))
           (aliases-boundedp-aux n aliases bound)))

Theorem: aliases-boundedp-aux-of-nfix-n

(defthm aliases-boundedp-aux-of-nfix-n
  (equal (aliases-boundedp-aux (nfix n)
                               aliases bound)
         (aliases-boundedp-aux n aliases bound)))

Theorem: aliases-boundedp-aux-nat-equiv-congruence-on-n

(defthm aliases-boundedp-aux-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (aliases-boundedp-aux n aliases bound)
                  (aliases-boundedp-aux n-equiv aliases bound)))
  :rule-classes :congruence)

Theorem: aliases-boundedp-aux-of-lhslist-fix-aliases

(defthm aliases-boundedp-aux-of-lhslist-fix-aliases
  (equal (aliases-boundedp-aux n (lhslist-fix aliases)
                               bound)
         (aliases-boundedp-aux n aliases bound)))

Theorem: aliases-boundedp-aux-lhslist-equiv-congruence-on-aliases

(defthm aliases-boundedp-aux-lhslist-equiv-congruence-on-aliases
  (implies (lhslist-equiv aliases aliases-equiv)
           (equal (aliases-boundedp-aux n aliases bound)
                  (aliases-boundedp-aux n aliases-equiv bound)))
  :rule-classes :congruence)

Theorem: aliases-boundedp-aux-of-nfix-bound

(defthm aliases-boundedp-aux-of-nfix-bound
  (equal (aliases-boundedp-aux n aliases (nfix bound))
         (aliases-boundedp-aux n aliases bound)))

Theorem: aliases-boundedp-aux-nat-equiv-congruence-on-bound

(defthm aliases-boundedp-aux-nat-equiv-congruence-on-bound
  (implies (nat-equiv bound bound-equiv)
           (equal (aliases-boundedp-aux n aliases bound)
                  (aliases-boundedp-aux n aliases bound-equiv)))
  :rule-classes :congruence)