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Substitution

Vl-repeateventcontrol-subst

Substitute into a vl-repeateventcontrol-p.

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

Definitions and Theorems

Function: vl-repeateventcontrol-subst

(defun vl-repeateventcontrol-subst (x sigma)
 (declare (xargs :guard (and (vl-repeateventcontrol-p x)
                             (vl-sigma-p sigma))))
 (declare (ignorable x sigma))
 (let ((__function__ 'vl-repeateventcontrol-subst))
   (declare (ignorable __function__))
   (change-vl-repeateventcontrol
        x
        :expr (vl-expr-subst (vl-repeateventcontrol->expr x)
                             sigma)
        :ctrl (vl-eventcontrol-subst (vl-repeateventcontrol->ctrl x)
                                     sigma))))

Theorem: vl-repeateventcontrol-p-of-vl-repeateventcontrol-subst

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

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

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

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

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

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

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

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

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