Get the sym field from a sym-prod.
(sym-prod->sym x) → sym
This is an ordinary field accessor created by defprod.
Function:
(defun sym-prod->sym$inline (x) (declare (xargs :guard (sym-prod-p x))) (declare (xargs :guard t)) (let ((acl2::__function__ 'sym-prod->sym)) (declare (ignorable acl2::__function__)) (mbe :logic (b* ((x (and t x))) (symbol-fix (cdr (std::da-nth 0 x)))) :exec (cdr (std::da-nth 0 x)))))
Theorem:
(defthm symbolp-of-sym-prod->sym (b* ((sym (sym-prod->sym$inline x))) (symbolp sym)) :rule-classes :rewrite)
Theorem:
(defthm sym-prod->sym$inline-of-sym-prod-fix-x (equal (sym-prod->sym$inline (sym-prod-fix x)) (sym-prod->sym$inline x)))
Theorem:
(defthm sym-prod->sym$inline-sym-prod-equiv-congruence-on-x (implies (sym-prod-equiv x x-equiv) (equal (sym-prod->sym$inline x) (sym-prod->sym$inline x-equiv))) :rule-classes :congruence)