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Symbolic-arithmetic

Bfr-loghead-ns

Signature
(bfr-loghead-ns n x) → xx
Arguments: n — Guard (natp n).; x — Guard (true-listp x).
Returns: xx — Type (true-listp xx).

Definitions and Theorems

Function: bfr-loghead-ns

(defun bfr-loghead-ns (n x)
  (declare (xargs :guard (and (natp n) (true-listp x))))
  (let ((__function__ 'bfr-loghead-ns))
    (declare (ignorable __function__))
    (b* (((when (zp n)) (bfr-sterm nil))
         ((mv head tail ?end)
          (first/rest/end x)))
      (bfr-scons head (bfr-loghead-ns (1- n) tail)))))

Theorem: true-listp-of-bfr-loghead-ns

(defthm true-listp-of-bfr-loghead-ns
  (b* ((xx (bfr-loghead-ns n x)))
    (true-listp xx))
  :rule-classes :type-prescription)

Theorem: bfr-loghead-ns-correct

(defthm bfr-loghead-ns-correct
  (b* ((xx (bfr-loghead-ns n x)))
    (and (equal (bfr-list->s xx env)
                (loghead (nfix n)
                         (bfr-list->s x env))))))

Theorem: bfr-loghead-ns-deps

(defthm bfr-loghead-ns-deps
  (b* ((xx (bfr-loghead-ns n x)))
    (implies (and (not (pbfr-list-depends-on varname param x)))
             (and (not (pbfr-list-depends-on varname param xx))))))