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Ctrex-rule

Ctrex-rule->order

Get the order field from a ctrex-rule.

Signature
(ctrex-rule->order x) → order
Arguments: x — Guard (ctrex-rule-p x).
Returns: order — Type (natp order).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: ctrex-rule->order$inline

(defun ctrex-rule->order$inline (x)
  (declare (xargs :guard (ctrex-rule-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'ctrex-rule->order))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (cdr (std::da-nth 9 x))))
         :exec (cdr (std::da-nth 9 x)))))

Theorem: natp-of-ctrex-rule->order

(defthm natp-of-ctrex-rule->order
  (b* ((order (ctrex-rule->order$inline x)))
    (natp order))
  :rule-classes :rewrite)

Theorem: ctrex-rule->order$inline-of-ctrex-rule-fix-x

(defthm ctrex-rule->order$inline-of-ctrex-rule-fix-x
  (equal (ctrex-rule->order$inline (ctrex-rule-fix x))
         (ctrex-rule->order$inline x)))

Theorem: ctrex-rule->order$inline-ctrex-rule-equiv-congruence-on-x

(defthm ctrex-rule->order$inline-ctrex-rule-equiv-congruence-on-x
  (implies (ctrex-rule-equiv x x-equiv)
           (equal (ctrex-rule->order$inline x)
                  (ctrex-rule->order$inline x-equiv)))
  :rule-classes :congruence)