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2vec

2vec-p

Recognizer for 2vecs.

Signature
(2vec-p x) → bool
Arguments: x — Guard (4vec-p x).

Definitions and Theorems

Function: 2vec-p$inline

(defun 2vec-p$inline (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '2vec-p))
    (declare (ignorable __function__))
    (mbe :logic (equal (4vec->upper x) (4vec->lower x))
         :exec (atom x))))

Theorem: 4vec->lower-when-2vec-p

(defthm 4vec->lower-when-2vec-p
  (implies (2vec-p x)
           (equal (4vec->lower x)
                  (4vec->upper x))))

Theorem: 2vec-p$inline-of-4vec-fix-x

(defthm 2vec-p$inline-of-4vec-fix-x
  (equal (2vec-p$inline (4vec-fix x))
         (2vec-p$inline x)))

Theorem: 2vec-p$inline-4vec-equiv-congruence-on-x

(defthm 2vec-p$inline-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (2vec-p$inline x)
                  (2vec-p$inline x-equiv)))
  :rule-classes :congruence)