Get the key field from a sd-problem.
(sd-problem->key x) → key
This is an ordinary field accessor created by defprod.
Function:
(defun sd-problem->key$inline (x) (declare (xargs :guard (sd-problem-p x))) (declare (xargs :guard t)) (let ((__function__ 'sd-problem->key)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and t x))) (sd-key-fix (car (cdr (cdr (cdr x)))))) :exec (car (cdr (cdr (cdr x)))))))
Theorem:
(defthm sd-key-p-of-sd-problem->key (b* ((key (sd-problem->key$inline x))) (sd-key-p key)) :rule-classes :rewrite)
Theorem:
(defthm sd-problem->key$inline-of-sd-problem-fix-x (equal (sd-problem->key$inline (sd-problem-fix x)) (sd-problem->key$inline x)))
Theorem:
(defthm sd-problem->key$inline-sd-problem-equiv-congruence-on-x (implies (sd-problem-equiv x x-equiv) (equal (sd-problem->key$inline x) (sd-problem->key$inline x-equiv))) :rule-classes :congruence)