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Lhbit-var

Lhbit-var->idx

Get the idx field from a lhbit-var.

Signature
(lhbit-var->idx x) → idx
Arguments: x — Guard (lhbit-p x).
Returns: idx — Type (natp idx).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhbit-var->idx$inline

(defun lhbit-var->idx$inline (x)
  (declare (xargs :guard (lhbit-p x)))
  (declare (xargs :guard (equal (lhbit-kind x) :var)))
  (let ((__function__ 'lhbit-var->idx))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (lhbit-kind x) :var) x)))
           (nfix (std::prod-cdr (cdr x))))
         :exec (std::prod-cdr (cdr x)))))

Theorem: natp-of-lhbit-var->idx

(defthm natp-of-lhbit-var->idx
  (b* ((idx (lhbit-var->idx$inline x)))
    (natp idx))
  :rule-classes :rewrite)

Theorem: lhbit-var->idx$inline-of-lhbit-fix-x

(defthm lhbit-var->idx$inline-of-lhbit-fix-x
  (equal (lhbit-var->idx$inline (lhbit-fix x))
         (lhbit-var->idx$inline x)))

Theorem: lhbit-var->idx$inline-lhbit-equiv-congruence-on-x

(defthm lhbit-var->idx$inline-lhbit-equiv-congruence-on-x
  (implies (lhbit-equiv x x-equiv)
           (equal (lhbit-var->idx$inline x)
                  (lhbit-var->idx$inline x-equiv)))
  :rule-classes :congruence)

Theorem: lhbit-var->idx-when-wrong-kind

(defthm lhbit-var->idx-when-wrong-kind
  (implies (not (equal (lhbit-kind x) :var))
           (equal (lhbit-var->idx x) (nfix nil))))