Get the tries-succ field from a prof-entry.
(prof-entry->tries-succ x) → tries-succ
This is an ordinary field accessor created by defprod.
Function:
(defun prof-entry->tries-succ$inline (x) (declare (xargs :guard (prof-entry-p x))) (declare (xargs :guard t)) (let ((__function__ 'prof-entry->tries-succ)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and t x))) (nfix (std::da-nth 1 x))) :exec (std::da-nth 1 x))))
Theorem:
(defthm natp-of-prof-entry->tries-succ (b* ((tries-succ (prof-entry->tries-succ$inline x))) (natp tries-succ)) :rule-classes :type-prescription)
Theorem:
(defthm prof-entry->tries-succ$inline-of-prof-entry-fix-x (equal (prof-entry->tries-succ$inline (prof-entry-fix x)) (prof-entry->tries-succ$inline x)))
Theorem:
(defthm prof-entry->tries-succ$inline-prof-entry-equiv-congruence-on-x (implies (prof-entry-equiv x x-equiv) (equal (prof-entry->tries-succ$inline x) (prof-entry->tries-succ$inline x-equiv))) :rule-classes :congruence)