Get the sub field from a proof-tree-relation.
(proof-tree-relation->sub x) → sub
This is an ordinary field accessor created by fty::defprod.
Function:
(defun proof-tree-relation->sub$inline (x) (declare (xargs :guard (proof-treep x))) (declare (xargs :guard (equal (proof-tree-kind x) :relation))) (let ((__function__ 'proof-tree-relation->sub)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (proof-tree-kind x) :relation) x))) (proof-tree-list-fix (std::da-nth 3 (cdr x)))) :exec (std::da-nth 3 (cdr x)))))
Theorem:
(defthm proof-tree-listp-of-proof-tree-relation->sub (b* ((sub (proof-tree-relation->sub$inline x))) (proof-tree-listp sub)) :rule-classes :rewrite)
Theorem:
(defthm proof-tree-relation->sub$inline-of-proof-tree-fix-x (equal (proof-tree-relation->sub$inline (proof-tree-fix x)) (proof-tree-relation->sub$inline x)))
Theorem:
(defthm proof-tree-relation->sub$inline-proof-tree-equiv-congruence-on-x (implies (proof-tree-equiv x x-equiv) (equal (proof-tree-relation->sub$inline x) (proof-tree-relation->sub$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm proof-tree-relation->sub-when-wrong-kind (implies (not (equal (proof-tree-kind x) :relation)) (equal (proof-tree-relation->sub x) (proof-tree-list-fix nil))))