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2vecnatx

2vecnatx-fix

Coerces an arbitrary 4vec into a 2vecnatx, by forcing any non-naturals to all Xes.

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

Definitions and Theorems

Function: 2vecnatx-fix

(defun 2vecnatx-fix (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '2vecnatx-fix))
    (declare (ignorable __function__))
    (if (and (2vec-p x) (<= 0 (2vec->val x)))
        (4vec-fix x)
      (4vec-x))))

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

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

Theorem: 2vecnatx-fix-of-2vecnatx-p

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

Theorem: 2vecnatx-fix-of-2vecx-fix-x

(defthm 2vecnatx-fix-of-2vecx-fix-x
  (equal (2vecnatx-fix (2vecx-fix x))
         (2vecnatx-fix x)))

Theorem: 2vecnatx-fix-2vecx-equiv-congruence-on-x

(defthm 2vecnatx-fix-2vecx-equiv-congruence-on-x
  (implies (2vecx-equiv x x-equiv)
           (equal (2vecnatx-fix x)
                  (2vecnatx-fix x-equiv)))
  :rule-classes :congruence)