Get the left field from a proof-tree-equal.
(proof-tree-equal->left x) → left
This is an ordinary field accessor created by fty::defprod.
Function:
(defun proof-tree-equal->left$inline (x) (declare (xargs :guard (proof-treep x))) (declare (xargs :guard (equal (proof-tree-kind x) :equal))) (let ((__function__ 'proof-tree-equal->left)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (proof-tree-kind x) :equal) x))) (expression-fix (std::da-nth 1 (cdr x)))) :exec (std::da-nth 1 (cdr x)))))
Theorem:
(defthm expressionp-of-proof-tree-equal->left (b* ((left (proof-tree-equal->left$inline x))) (expressionp left)) :rule-classes :rewrite)
Theorem:
(defthm proof-tree-equal->left$inline-of-proof-tree-fix-x (equal (proof-tree-equal->left$inline (proof-tree-fix x)) (proof-tree-equal->left$inline x)))
Theorem:
(defthm proof-tree-equal->left$inline-proof-tree-equiv-congruence-on-x (implies (proof-tree-equiv x x-equiv) (equal (proof-tree-equal->left$inline x) (proof-tree-equal->left$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm proof-tree-equal->left-when-wrong-kind (implies (not (equal (proof-tree-kind x) :equal)) (equal (proof-tree-equal->left x) (expression-fix nil))))