Get the left field from a axi-gate.
(axi-gate->left x) → left
This is an ordinary field accessor created by fty::defprod.
Function:
(defun axi-gate->left$inline (x) (declare (xargs :guard (axi-term-p x))) (declare (xargs :guard (equal (axi-term-kind x) :gate))) (let ((__function__ 'axi-gate->left)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (axi-term-kind x) :gate) x))) (axi-lit-fix (cadr x))) :exec (cadr x))))
Theorem:
(defthm axi-lit-p-of-axi-gate->left (b* ((left (axi-gate->left$inline x))) (axi-lit-p left)) :rule-classes :rewrite)
Theorem:
(defthm axi-gate->left$inline-of-axi-term-fix-x (equal (axi-gate->left$inline (axi-term-fix x)) (axi-gate->left$inline x)))
Theorem:
(defthm axi-gate->left$inline-axi-term-equiv-congruence-on-x (implies (axi-term-equiv x x-equiv) (equal (axi-gate->left$inline x) (axi-gate->left$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm axi-gate->left-when-wrong-kind (implies (not (equal (axi-term-kind x) :gate)) (equal (axi-gate->left x) (axi-lit-fix nil))))