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Substitution

Vl-paramdecl-subst

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

Definitions and Theorems

Function: vl-paramdecl-subst

(defun vl-paramdecl-subst (x sigma)
 (declare (xargs :guard (and (vl-paramdecl-p x)
                             (vl-sigma-p sigma))))
 (declare (ignorable x sigma))
 (let ((__function__ 'vl-paramdecl-subst))
  (declare (ignorable __function__))
  (b* (((vl-paramdecl x) x))
    (change-vl-paramdecl x
                         :type (vl-paramtype-subst x.type sigma)))))

Theorem: vl-paramdecl-p-of-vl-paramdecl-subst

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

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

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

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

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

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

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

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

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