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S4vecs

S2vec-p

Signature
(s2vec-p x) → *
Arguments: x — Guard (s4vec-p x).

Definitions and Theorems

Function: s2vec-p$inline

(defun s2vec-p$inline (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's2vec-p))
    (declare (ignorable __function__))
    (mbe :logic
         (b* (((s4vec x)))
           (equal x.upper x.lower))
         :exec (or (atom x) (not (cdr x))))))

Theorem: s2vec-p$inline-of-s4vec-fix-x

(defthm s2vec-p$inline-of-s4vec-fix-x
  (equal (s2vec-p$inline (s4vec-fix x))
         (s2vec-p$inline x)))

Theorem: s2vec-p$inline-s4vec-equiv-congruence-on-x

(defthm s2vec-p$inline-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s2vec-p$inline x)
                  (s2vec-p$inline x-equiv)))
  :rule-classes :congruence)