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Fraig-config

Fraig-config->gatesimp

Get the gatesimp field from a fraig-config.

Signature
(fraig-config->gatesimp x) → gatesimp
Arguments: x — Guard (fraig-config-p x).
Returns: gatesimp — Type (gatesimp-p gatesimp).

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

Definitions and Theorems

Function: fraig-config->gatesimp$inline

(defun fraig-config->gatesimp$inline (x)
  (declare (xargs :guard (fraig-config-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'fraig-config->gatesimp))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (gatesimp-fix (cdr (std::da-nth 12 (cdr x)))))
         :exec (cdr (std::da-nth 12 (cdr x))))))

Theorem: gatesimp-p-of-fraig-config->gatesimp

(defthm gatesimp-p-of-fraig-config->gatesimp
  (b* ((gatesimp (fraig-config->gatesimp$inline x)))
    (gatesimp-p gatesimp))
  :rule-classes :rewrite)

Theorem: fraig-config->gatesimp$inline-of-fraig-config-fix-x

(defthm fraig-config->gatesimp$inline-of-fraig-config-fix-x
  (equal (fraig-config->gatesimp$inline (fraig-config-fix x))
         (fraig-config->gatesimp$inline x)))

Theorem: fraig-config->gatesimp$inline-fraig-config-equiv-congruence-on-x

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