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A4vec

A4vec->lower

Get the lower field from a a4vec.

Signature
(a4vec->lower x) → lower
Arguments: x — Guard (a4vec-p x).
Returns: lower — Type (true-listp lower).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: a4vec->lower$inline

(defun a4vec->lower$inline (x)
  (declare (xargs :guard (a4vec-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'a4vec->lower))
    (declare (ignorable __function__))
    (mbe :logic (b* ((x (and t x))) (list-fix (cdr x)))
         :exec (cdr x))))

Theorem: true-listp-of-a4vec->lower

(defthm true-listp-of-a4vec->lower
  (b* ((lower (a4vec->lower$inline x)))
    (true-listp lower))
  :rule-classes :rewrite)

Theorem: a4vec->lower$inline-of-a4vec-fix-x

(defthm a4vec->lower$inline-of-a4vec-fix-x
  (equal (a4vec->lower$inline (a4vec-fix x))
         (a4vec->lower$inline x)))

Theorem: a4vec->lower$inline-a4vec-equiv-congruence-on-x

(defthm a4vec->lower$inline-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a4vec->lower$inline x)
                  (a4vec->lower$inline x-equiv)))
  :rule-classes :congruence)