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• Svex-select

Svex-select-to-svex-with-substitution

Signature

(svex-select-to-svex-with-substitution x subst) → svex-x

Arguments

x — Guard (svex-select-p x).

subst — Guard (svex-p subst).

Returns

svex-x — Type (svex-p svex-x).

Definitions and Theorems

Function: svex-select-to-svex-with-substitution

(defun svex-select-to-svex-with-substitution (x subst)
 (declare (xargs :guard (and (svex-select-p x) (svex-p subst))))
 (let ((__function__ 'svex-select-to-svex-with-substitution))
  (declare (ignorable __function__))
  (svex-select-case
    x
    :var (svex-fix subst)
    :part
    (svcall
         partsel x.lsb (svex-int x.width)
         (svex-concat
              (svex-select->width x.subexp)
              (svex-select-to-svex-with-substitution x.subexp subst)
              (svex-x))))))

Theorem: svex-p-of-svex-select-to-svex-with-substitution

(defthm svex-p-of-svex-select-to-svex-with-substitution
  (b* ((svex-x (svex-select-to-svex-with-substitution x subst)))
    (svex-p svex-x))
  :rule-classes :rewrite)

Theorem: svex-select-to-svex-with-substitution-of-svex-select-fix-x

(defthm svex-select-to-svex-with-substitution-of-svex-select-fix-x
  (equal (svex-select-to-svex-with-substitution (svex-select-fix x)
                                                subst)
         (svex-select-to-svex-with-substitution x subst)))

Theorem: svex-select-to-svex-with-substitution-svex-select-equiv-congruence-on-x

(defthm
 svex-select-to-svex-with-substitution-svex-select-equiv-congruence-on-x
 (implies
      (svex-select-equiv x x-equiv)
      (equal (svex-select-to-svex-with-substitution x subst)
             (svex-select-to-svex-with-substitution x-equiv subst)))
 :rule-classes :congruence)

Theorem: svex-select-to-svex-with-substitution-of-svex-fix-subst

(defthm svex-select-to-svex-with-substitution-of-svex-fix-subst
  (equal (svex-select-to-svex-with-substitution x (svex-fix subst))
         (svex-select-to-svex-with-substitution x subst)))

Theorem: svex-select-to-svex-with-substitution-svex-equiv-congruence-on-subst

(defthm
 svex-select-to-svex-with-substitution-svex-equiv-congruence-on-subst
 (implies
      (svex-equiv subst subst-equiv)
      (equal (svex-select-to-svex-with-substitution x subst)
             (svex-select-to-svex-with-substitution x subst-equiv)))
 :rule-classes :congruence)