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• Obs-constprop-config

Obs-constprop-config->gatesimp

Get the gatesimp field from a obs-constprop-config.

Signature

(obs-constprop-config->gatesimp x) → gatesimp

Arguments

x — Guard (obs-constprop-config-p x).

Returns

gatesimp — Type (gatesimp-p gatesimp).

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

Definitions and Theorems

Function: obs-constprop-config->gatesimp$inline

(defun obs-constprop-config->gatesimp$inline (x)
  (declare (xargs :guard (obs-constprop-config-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'obs-constprop-config->gatesimp))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (gatesimp-fix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: gatesimp-p-of-obs-constprop-config->gatesimp

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

Theorem: obs-constprop-config->gatesimp$inline-of-obs-constprop-config-fix-x

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

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

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