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Rule

Rule->definiens

Get the definiens field from a rule.

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

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

Definitions and Theorems

Function: rule->definiens$inline

(defun rule->definiens$inline (x)
  (declare (xargs :guard (rulep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'rule->definiens))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (alternation-fix (std::da-nth 2 (cdr x))))
         :exec (std::da-nth 2 (cdr x)))))

Theorem: alternationp-of-rule->definiens

(defthm alternationp-of-rule->definiens
  (b* ((definiens (rule->definiens$inline x)))
    (alternationp definiens))
  :rule-classes :rewrite)

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

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

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

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