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• Sv::vl-expr.lisp

Svex-repeat-aux

Signature

(svex-repeat-aux n width x acc) → concat

Arguments

n — Guard (natp n).

width — Guard (natp width).

x — Guard (sv::svex-p x).

acc — Guard (sv::svex-p acc).

Returns

concat — Type (sv::svex-p concat).

Definitions and Theorems

Function: svex-repeat-aux

(defun svex-repeat-aux (n width x acc)
  (declare (xargs :guard (and (natp n)
                              (natp width)
                              (sv::svex-p x)
                              (sv::svex-p acc))))
  (let ((__function__ 'svex-repeat-aux))
    (declare (ignorable __function__))
    (if (zp n)
        (sv::svex-fix acc)
      (svex-repeat-aux (1- n)
                       width x
                       (sv::svex-concat (lnfix width)
                                        x acc)))))

Theorem: svex-p-of-svex-repeat-aux

(defthm svex-p-of-svex-repeat-aux
  (b* ((concat (svex-repeat-aux n width x acc)))
    (sv::svex-p concat))
  :rule-classes :rewrite)

Theorem: vars-of-svex-repeat-aux

(defthm vars-of-svex-repeat-aux
  (b* ((?concat (svex-repeat-aux n width x acc)))
    (implies (and (not (member v (sv::svex-vars x)))
                  (not (member v (sv::svex-vars acc))))
             (not (member v (sv::svex-vars concat))))))

Theorem: svex-repeat-aux-of-nfix-n

(defthm svex-repeat-aux-of-nfix-n
  (equal (svex-repeat-aux (nfix n) width x acc)
         (svex-repeat-aux n width x acc)))

Theorem: svex-repeat-aux-nat-equiv-congruence-on-n

(defthm svex-repeat-aux-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (svex-repeat-aux n width x acc)
                  (svex-repeat-aux n-equiv width x acc)))
  :rule-classes :congruence)

Theorem: svex-repeat-aux-of-nfix-width

(defthm svex-repeat-aux-of-nfix-width
  (equal (svex-repeat-aux n (nfix width) x acc)
         (svex-repeat-aux n width x acc)))

Theorem: svex-repeat-aux-nat-equiv-congruence-on-width

(defthm svex-repeat-aux-nat-equiv-congruence-on-width
  (implies (acl2::nat-equiv width width-equiv)
           (equal (svex-repeat-aux n width x acc)
                  (svex-repeat-aux n width-equiv x acc)))
  :rule-classes :congruence)

Theorem: svex-repeat-aux-of-svex-fix-x

(defthm svex-repeat-aux-of-svex-fix-x
  (equal (svex-repeat-aux n width (sv::svex-fix x)
                          acc)
         (svex-repeat-aux n width x acc)))

Theorem: svex-repeat-aux-svex-equiv-congruence-on-x

(defthm svex-repeat-aux-svex-equiv-congruence-on-x
  (implies (sv::svex-equiv x x-equiv)
           (equal (svex-repeat-aux n width x acc)
                  (svex-repeat-aux n width x-equiv acc)))
  :rule-classes :congruence)

Theorem: svex-repeat-aux-of-svex-fix-acc

(defthm svex-repeat-aux-of-svex-fix-acc
  (equal (svex-repeat-aux n width x (sv::svex-fix acc))
         (svex-repeat-aux n width x acc)))

Theorem: svex-repeat-aux-svex-equiv-congruence-on-acc

(defthm svex-repeat-aux-svex-equiv-congruence-on-acc
  (implies (sv::svex-equiv acc acc-equiv)
           (equal (svex-repeat-aux n width x acc)
                  (svex-repeat-aux n width x acc-equiv)))
  :rule-classes :congruence)