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• Sv::vl-expr.lisp

Svex-multiconcat

Signature

(svex-multiconcat n x widths) → concat

Arguments

n — Guard (natp n).

x — Guard (sv::svexlist-p x).

widths — Guard (nat-listp widths).

Returns

concat — Type (sv::svex-p concat).

Definitions and Theorems

Function: svex-multiconcat

(defun svex-multiconcat (n x widths)
  (declare (xargs :guard (and (natp n)
                              (sv::svexlist-p x)
                              (nat-listp widths))))
  (declare (xargs :guard (eql (len x) (len widths))))
  (let ((__function__ 'svex-multiconcat))
    (declare (ignorable __function__))
    (svex-repeat n (sum-nats widths)
                 (svex-concat-list widths x))))

Theorem: svex-p-of-svex-multiconcat

(defthm svex-p-of-svex-multiconcat
  (b* ((concat (svex-multiconcat n x widths)))
    (sv::svex-p concat))
  :rule-classes :rewrite)

Theorem: vars-of-svex-multiconcat

(defthm vars-of-svex-multiconcat
  (b* ((?concat (svex-multiconcat n x widths)))
    (implies (not (member v (sv::svexlist-vars x)))
             (not (member v (sv::svex-vars concat))))))

Theorem: svex-multiconcat-of-nfix-n

(defthm svex-multiconcat-of-nfix-n
  (equal (svex-multiconcat (nfix n) x widths)
         (svex-multiconcat n x widths)))

Theorem: svex-multiconcat-nat-equiv-congruence-on-n

(defthm svex-multiconcat-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (svex-multiconcat n x widths)
                  (svex-multiconcat n-equiv x widths)))
  :rule-classes :congruence)

Theorem: svex-multiconcat-of-svexlist-fix-x

(defthm svex-multiconcat-of-svexlist-fix-x
  (equal (svex-multiconcat n (sv::svexlist-fix x)
                           widths)
         (svex-multiconcat n x widths)))

Theorem: svex-multiconcat-svexlist-equiv-congruence-on-x

(defthm svex-multiconcat-svexlist-equiv-congruence-on-x
  (implies (sv::svexlist-equiv x x-equiv)
           (equal (svex-multiconcat n x widths)
                  (svex-multiconcat n x-equiv widths)))
  :rule-classes :congruence)