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• Substitution

Vl-arguments-subst

Substitute into a vl-arguments-p.

Signature

(vl-arguments-subst x sigma) → new-x

Arguments

x — Guard (vl-arguments-p x).

sigma — Guard (vl-sigma-p sigma).

Returns

new-x — Type (vl-arguments-p new-x).

Definitions and Theorems

Function: vl-arguments-subst

(defun vl-arguments-subst (x sigma)
  (declare (xargs :guard (and (vl-arguments-p x)
                              (vl-sigma-p sigma))))
  (declare (ignorable x sigma))
  (let ((__function__ 'vl-arguments-subst))
    (declare (ignorable __function__))
    (vl-arguments-case
         x
         :vl-arguments-named
         (change-vl-arguments-named
              x
              :args (vl-namedarglist-subst x.args sigma))
         :vl-arguments-plain
         (change-vl-arguments-plain
              x
              :args (vl-plainarglist-subst x.args sigma)))))

Theorem: vl-arguments-p-of-vl-arguments-subst

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

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

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

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

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

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

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

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

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