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