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Vttree-branch

Vttree-branch->left

Get the left field from a vttree-branch.

Signature
(vttree-branch->left x) → left
Arguments: x — Guard (vttree-p x).
Returns: left — Type (vttree-p left).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: vttree-branch->left$inline

(defun vttree-branch->left$inline (x)
  (declare (xargs :guard (vttree-p x)))
  (declare (xargs :guard (equal (vttree-kind x) :branch)))
  (let ((__function__ 'vttree-branch->left))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (vttree-kind x) :branch)
                      x)))
           (vttree-fix (car x)))
         :exec (car x))))

Theorem: vttree-p-of-vttree-branch->left

(defthm vttree-p-of-vttree-branch->left
  (b* ((left (vttree-branch->left$inline x)))
    (vttree-p left))
  :rule-classes :rewrite)

Theorem: vttree-branch->left$inline-of-vttree-fix-x

(defthm vttree-branch->left$inline-of-vttree-fix-x
  (equal (vttree-branch->left$inline (vttree-fix x))
         (vttree-branch->left$inline x)))

Theorem: vttree-branch->left$inline-vttree-equiv-congruence-on-x

(defthm vttree-branch->left$inline-vttree-equiv-congruence-on-x
  (implies (vttree-equiv x x-equiv)
           (equal (vttree-branch->left$inline x)
                  (vttree-branch->left$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vttree-branch->left-when-wrong-kind

(defthm vttree-branch->left-when-wrong-kind
  (implies (not (equal (vttree-kind x) :branch))
           (equal (vttree-branch->left x)
                  (vttree-fix nil))))