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Rule

Rule->incremental

Get the incremental field from a rule.

Signature
(rule->incremental x) → incremental
Arguments: x — Guard (rulep x).
Returns: incremental — Type (booleanp incremental).

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

Definitions and Theorems

Function: rule->incremental$inline

(defun rule->incremental$inline (x)
  (declare (xargs :guard (rulep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'rule->incremental))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::bool-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: booleanp-of-rule->incremental

(defthm booleanp-of-rule->incremental
  (b* ((incremental (rule->incremental$inline x)))
    (booleanp incremental))
  :rule-classes :rewrite)

Theorem: rule->incremental$inline-of-rule-fix-x

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

Theorem: rule->incremental$inline-rule-equiv-congruence-on-x

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