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Ex-args

Ex-args->fn-lvls

Get the fn-lvls field from a ex-args.

Signature
(ex-args->fn-lvls x) → fn-lvls
Arguments: x — Guard (ex-args-p x).
Returns: fn-lvls — Type (sym-nat-alistp fn-lvls).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: ex-args->fn-lvls$inline

(defun ex-args->fn-lvls$inline (x)
  (declare (xargs :guard (ex-args-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'ex-args->fn-lvls))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (sym-nat-alist-fix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: sym-nat-alistp-of-ex-args->fn-lvls

(defthm sym-nat-alistp-of-ex-args->fn-lvls
  (b* ((fn-lvls (ex-args->fn-lvls$inline x)))
    (sym-nat-alistp fn-lvls))
  :rule-classes :rewrite)

Theorem: ex-args->fn-lvls$inline-of-ex-args-fix-x

(defthm ex-args->fn-lvls$inline-of-ex-args-fix-x
  (equal (ex-args->fn-lvls$inline (ex-args-fix x))
         (ex-args->fn-lvls$inline x)))

Theorem: ex-args->fn-lvls$inline-ex-args-equiv-congruence-on-x

(defthm ex-args->fn-lvls$inline-ex-args-equiv-congruence-on-x
  (implies (ex-args-equiv x x-equiv)
           (equal (ex-args->fn-lvls$inline x)
                  (ex-args->fn-lvls$inline x-equiv)))
  :rule-classes :congruence)