Get the arg-contexts field from a congruence-rule.
(congruence-rule->arg-contexts x) → arg-contexts
This is an ordinary field accessor created by defprod.
Function:
(defun congruence-rule->arg-contexts$inline (x) (declare (xargs :guard (congruence-rule-p x))) (declare (xargs :guard t)) (let ((__function__ 'congruence-rule->arg-contexts)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and t x))) (equiv-contextslist-fix (std::da-nth 2 x))) :exec (std::da-nth 2 x))))
Theorem:
(defthm equiv-contextslist-p-of-congruence-rule->arg-contexts (b* ((arg-contexts (congruence-rule->arg-contexts$inline x))) (equiv-contextslist-p arg-contexts)) :rule-classes :rewrite)
Theorem:
(defthm congruence-rule->arg-contexts$inline-of-congruence-rule-fix-x (equal (congruence-rule->arg-contexts$inline (congruence-rule-fix x)) (congruence-rule->arg-contexts$inline x)))
Theorem:
(defthm congruence-rule->arg-contexts$inline-congruence-rule-equiv-congruence-on-x (implies (congruence-rule-equiv x x-equiv) (equal (congruence-rule->arg-contexts$inline x) (congruence-rule->arg-contexts$inline x-equiv))) :rule-classes :congruence)