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Scopesubst

Vl-initial-scopesubst

Scopesubstitute into a vl-initial-p.

Signature
(vl-initial-scopesubst x ss) → new-x
Arguments: x — Guard (vl-initial-p x).; ss — Guard (vl-scopestack-p ss).
Returns: new-x — Type (vl-initial-p new-x).

Definitions and Theorems

Function: vl-initial-scopesubst

(defun vl-initial-scopesubst (x ss)
 (declare (xargs :guard (and (vl-initial-p x)
                             (vl-scopestack-p ss))))
 (declare (ignorable x ss))
 (let ((__function__ 'vl-initial-scopesubst))
   (declare (ignorable __function__))
   (change-vl-initial x
                      :stmt (vl-stmt-scopesubst (vl-initial->stmt x)
                                                ss))))

Theorem: vl-initial-p-of-vl-initial-scopesubst

(defthm vl-initial-p-of-vl-initial-scopesubst
  (b* ((new-x (vl-initial-scopesubst x ss)))
    (vl-initial-p new-x))
  :rule-classes :rewrite)

Theorem: vl-initial-scopesubst-of-vl-initial-fix-x

(defthm vl-initial-scopesubst-of-vl-initial-fix-x
  (equal (vl-initial-scopesubst (vl-initial-fix x)
                                ss)
         (vl-initial-scopesubst x ss)))

Theorem: vl-initial-scopesubst-vl-initial-equiv-congruence-on-x

(defthm vl-initial-scopesubst-vl-initial-equiv-congruence-on-x
  (implies (vl-initial-equiv x x-equiv)
           (equal (vl-initial-scopesubst x ss)
                  (vl-initial-scopesubst x-equiv ss)))
  :rule-classes :congruence)

Theorem: vl-initial-scopesubst-of-vl-scopestack-fix-ss

(defthm vl-initial-scopesubst-of-vl-scopestack-fix-ss
  (equal (vl-initial-scopesubst x (vl-scopestack-fix ss))
         (vl-initial-scopesubst x ss)))

Theorem: vl-initial-scopesubst-vl-scopestack-equiv-congruence-on-ss

(defthm vl-initial-scopesubst-vl-scopestack-equiv-congruence-on-ss
  (implies (vl-scopestack-equiv ss ss-equiv)
           (equal (vl-initial-scopesubst x ss)
                  (vl-initial-scopesubst x ss-equiv)))
  :rule-classes :congruence)