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S4vecs

S2vec

Signature
(s2vec x) → result
Arguments: x — Guard (sparseint-p x).
Returns: result — Type (s4vec-p result).

Definitions and Theorems

Function: s2vec

(defun s2vec (x)
  (declare (xargs :guard (sparseint-p x)))
  (let ((__function__ 's2vec))
    (declare (ignorable __function__))
    (mbe :logic (s4vec x x)
         :exec
         (b* ((x (sparseint-fix x)))
           (if (integerp x) x (list x))))))

Theorem: s4vec-p-of-s2vec

(defthm s4vec-p-of-s2vec
  (b* ((result (s2vec x)))
    (s4vec-p result))
  :rule-classes :rewrite)

Theorem: s4vec->upper-of-s2vec

(defthm s4vec->upper-of-s2vec
  (b* ((?result (s2vec x)))
    (equal (s4vec->upper result)
           (sparseint-fix x))))

Theorem: s4vec->lower-of-s2vec

(defthm s4vec->lower-of-s2vec
  (b* ((?result (s2vec x)))
    (equal (s4vec->lower result)
           (sparseint-fix x))))

Theorem: s2vec-of-sparseint-fix-x

(defthm s2vec-of-sparseint-fix-x
  (equal (s2vec (sparseint-fix x))
         (s2vec x)))

Theorem: s2vec-sparseint-equiv-congruence-on-x

(defthm s2vec-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (s2vec x) (s2vec x-equiv)))
  :rule-classes :congruence)