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Scopesubst

Vl-evatom-scopesubst

Scopesubstitute into a vl-evatom-p.

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

Definitions and Theorems

Function: vl-evatom-scopesubst

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

Theorem: vl-evatom-p-of-vl-evatom-scopesubst

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

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

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

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

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

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

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

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

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