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Deftreeops-rulename-info

Deftreeops-rulename-info->alt-kind

Get the alt-kind field from a deftreeops-rulename-info.

Signature
(deftreeops-rulename-info->alt-kind x) → alt-kind
Arguments: x — Guard (deftreeops-rulename-infop x).
Returns: alt-kind — Type (natp alt-kind).

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

Definitions and Theorems

Function: deftreeops-rulename-info->alt-kind$inline

(defun deftreeops-rulename-info->alt-kind$inline (x)
  (declare (xargs :guard (deftreeops-rulename-infop x)))
  (declare (xargs :guard t))
  (let ((__function__ 'deftreeops-rulename-info->alt-kind))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (cdr (std::da-nth 6 x))))
         :exec (cdr (std::da-nth 6 x)))))

Theorem: natp-of-deftreeops-rulename-info->alt-kind

(defthm natp-of-deftreeops-rulename-info->alt-kind
  (b* ((alt-kind (deftreeops-rulename-info->alt-kind$inline x)))
    (natp alt-kind))
  :rule-classes :rewrite)

Theorem: deftreeops-rulename-info->alt-kind$inline-of-deftreeops-rulename-info-fix-x

(defthm
 deftreeops-rulename-info->alt-kind$inline-of-deftreeops-rulename-info-fix-x
 (equal (deftreeops-rulename-info->alt-kind$inline
             (deftreeops-rulename-info-fix x))
        (deftreeops-rulename-info->alt-kind$inline x)))

Theorem: deftreeops-rulename-info->alt-kind$inline-deftreeops-rulename-info-equiv-congruence-on-x

(defthm
 deftreeops-rulename-info->alt-kind$inline-deftreeops-rulename-info-equiv-congruence-on-x
 (implies
      (deftreeops-rulename-info-equiv x x-equiv)
      (equal (deftreeops-rulename-info->alt-kind$inline x)
             (deftreeops-rulename-info->alt-kind$inline x-equiv)))
 :rule-classes :congruence)