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• Substitution

Vl-packeddimension-subst

Substitute into a vl-packeddimension-p.

Signature

(vl-packeddimension-subst x sigma) → new-x

Arguments

x — Guard (vl-packeddimension-p x).

sigma — Guard (vl-sigma-p sigma).

Returns

new-x — Type (vl-packeddimension-p new-x).

Definitions and Theorems

Function: vl-packeddimension-subst

(defun vl-packeddimension-subst (x sigma)
  (declare (xargs :guard (and (vl-packeddimension-p x)
                              (vl-sigma-p sigma))))
  (declare (ignorable x sigma))
  (let ((__function__ 'vl-packeddimension-subst))
    (declare (ignorable __function__))
    (b* ((x (vl-packeddimension-fix x)))
      (if (eq x :vl-unsized-dimension)
          x
        (vl-range-subst x sigma)))))

Theorem: vl-packeddimension-p-of-vl-packeddimension-subst

(defthm vl-packeddimension-p-of-vl-packeddimension-subst
  (b* ((new-x (vl-packeddimension-subst x sigma)))
    (vl-packeddimension-p new-x))
  :rule-classes :rewrite)

Theorem: vl-packeddimension-subst-of-vl-packeddimension-fix-x

(defthm vl-packeddimension-subst-of-vl-packeddimension-fix-x
  (equal (vl-packeddimension-subst (vl-packeddimension-fix x)
                                   sigma)
         (vl-packeddimension-subst x sigma)))

Theorem: vl-packeddimension-subst-vl-packeddimension-equiv-congruence-on-x

(defthm
  vl-packeddimension-subst-vl-packeddimension-equiv-congruence-on-x
  (implies (vl-packeddimension-equiv x x-equiv)
           (equal (vl-packeddimension-subst x sigma)
                  (vl-packeddimension-subst x-equiv sigma)))
  :rule-classes :congruence)

Theorem: vl-packeddimension-subst-of-vl-sigma-fix-sigma

(defthm vl-packeddimension-subst-of-vl-sigma-fix-sigma
  (equal (vl-packeddimension-subst x (vl-sigma-fix sigma))
         (vl-packeddimension-subst x sigma)))

Theorem: vl-packeddimension-subst-vl-sigma-equiv-congruence-on-sigma

(defthm vl-packeddimension-subst-vl-sigma-equiv-congruence-on-sigma
  (implies (vl-sigma-equiv sigma sigma-equiv)
           (equal (vl-packeddimension-subst x sigma)
                  (vl-packeddimension-subst x sigma-equiv)))
  :rule-classes :congruence)