Get the left field from a bexp-equal.
This is an ordinary field accessor created by fty::defprod.
Function:
(defun bexp-equal->left$inline (x) (declare (xargs :guard (bexpp x))) (declare (xargs :guard (equal (bexp-kind x) :equal))) (let ((__function__ 'bexp-equal->left)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (bexp-kind x) :equal) x))) (aexp-fix (std::da-nth 0 (cdr x)))) :exec (std::da-nth 0 (cdr x)))))
Theorem:
(defthm aexpp-of-bexp-equal->left (b* ((left (bexp-equal->left$inline x))) (aexpp left)) :rule-classes :rewrite)
Theorem:
(defthm bexp-equal->left$inline-of-bexp-fix-x (equal (bexp-equal->left$inline (bexp-fix x)) (bexp-equal->left$inline x)))
Theorem:
(defthm bexp-equal->left$inline-bexp-equiv-congruence-on-x (implies (bexp-equiv x x-equiv) (equal (bexp-equal->left$inline x) (bexp-equal->left$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm bexp-equal->left-when-wrong-kind (implies (not (equal (bexp-kind x) :equal)) (equal (bexp-equal->left x) (aexp-fix nil))))