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Vars+modes

Vars+modes->vars

Get the vars field from a vars+modes.

Signature
(vars+modes->vars x) → vars
Arguments: x — Guard (vars+modes-p x).
Returns: vars — Type (identifier-setp vars).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: vars+modes->vars$inline

(defun vars+modes->vars$inline (x)
  (declare (xargs :guard (vars+modes-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vars+modes->vars))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (identifier-set-fix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: identifier-setp-of-vars+modes->vars

(defthm identifier-setp-of-vars+modes->vars
  (b* ((vars (vars+modes->vars$inline x)))
    (identifier-setp vars))
  :rule-classes :rewrite)

Theorem: vars+modes->vars$inline-of-vars+modes-fix-x

(defthm vars+modes->vars$inline-of-vars+modes-fix-x
  (equal (vars+modes->vars$inline (vars+modes-fix x))
         (vars+modes->vars$inline x)))

Theorem: vars+modes->vars$inline-vars+modes-equiv-congruence-on-x

(defthm vars+modes->vars$inline-vars+modes-equiv-congruence-on-x
  (implies (vars+modes-equiv x x-equiv)
           (equal (vars+modes->vars$inline x)
                  (vars+modes->vars$inline x-equiv)))
  :rule-classes :congruence)