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2vecx

2vecx-fix

Coerces an arbitrary 4vec to a 2vecx, by forcing any non-2vecs to an just be infinite Xes.

Signature
(2vecx-fix x) → x-fix
Arguments: x — Guard (4vec-p x).
Returns: x-fix — Type (2vecx-p! x-fix).

Definitions and Theorems

Function: 2vecx-fix$inline

(defun 2vecx-fix$inline (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '2vecx-fix))
    (declare (ignorable __function__))
    (if (2vec-p x) (4vec-fix x) (4vec-x))))

Theorem: 2vecx-p!-of-2vecx-fix

(defthm 2vecx-p!-of-2vecx-fix
  (b* ((x-fix (2vecx-fix$inline x)))
    (2vecx-p! x-fix))
  :rule-classes :rewrite)

Theorem: 2vecx-fix-of-2vecx-p

(defthm 2vecx-fix-of-2vecx-p
  (implies (2vecx-p x)
           (equal (2vecx-fix x) (4vec-fix x))))

Theorem: 2vecx-fix$inline-of-3vec-fix-x

(defthm 2vecx-fix$inline-of-3vec-fix-x
  (equal (2vecx-fix$inline (3vec-fix x))
         (2vecx-fix$inline x)))

Theorem: 2vecx-fix$inline-3vec-equiv-congruence-on-x

(defthm 2vecx-fix$inline-3vec-equiv-congruence-on-x
  (implies (3vec-equiv x x-equiv)
           (equal (2vecx-fix$inline x)
                  (2vecx-fix$inline x-equiv)))
  :rule-classes :congruence)