		Search-engine friendly clone of the ACL2 documentation.

Substitution

Vl-port-subst

Substitute into a vl-port-p.

Signature
(vl-port-subst x sigma) → new-x
Arguments: x — Guard (vl-port-p x).; sigma — Guard (vl-sigma-p sigma).
Returns: new-x — Type (vl-port-p new-x).

Definitions and Theorems

Function: vl-port-subst

(defun vl-port-subst (x sigma)
  (declare (xargs :guard (and (vl-port-p x) (vl-sigma-p sigma))))
  (declare (ignorable x sigma))
  (let ((__function__ 'vl-port-subst))
    (declare (ignorable __function__))
    (b* ((x (vl-port-fix x)))
      (case (tag x)
            (:vl-interfaceport (vl-interfaceport-subst x sigma))
            (otherwise (vl-regularport-subst x sigma))))))

Theorem: vl-port-p-of-vl-port-subst

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

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

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

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

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

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

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

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

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