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And-node

And-node->fanin0

Get the fanin0 field from a and-node.

Signature
(and-node->fanin0 x) → fanin0
Arguments: x — Guard (node-p x).
Returns: fanin0 — Type (litp fanin0).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: and-node->fanin0$inline

(defun and-node->fanin0$inline (x)
  (declare (xargs :guard (node-p x)))
  (declare (xargs :guard (equal (stype x) :and)))
  (let ((__function__ 'and-node->fanin0))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (stype x) :and) x)))
           (lit-fix (cadr x)))
         :exec (cadr x))))

Theorem: litp-of-and-node->fanin0

(defthm litp-of-and-node->fanin0
  (b* ((fanin0 (and-node->fanin0$inline x)))
    (litp fanin0))
  :rule-classes :type-prescription)

Theorem: and-node->fanin0$inline-of-node-fix-x

(defthm and-node->fanin0$inline-of-node-fix-x
  (equal (and-node->fanin0$inline (node-fix x))
         (and-node->fanin0$inline x)))

Theorem: and-node->fanin0$inline-node-equiv-congruence-on-x

(defthm and-node->fanin0$inline-node-equiv-congruence-on-x
  (implies (node-equiv x x-equiv)
           (equal (and-node->fanin0$inline x)
                  (and-node->fanin0$inline x-equiv)))
  :rule-classes :congruence)

Theorem: and-node->fanin0-when-wrong-kind

(defthm and-node->fanin0-when-wrong-kind
  (implies (not (equal (stype x) :and))
           (equal (and-node->fanin0 x)
                  (lit-fix nil))))