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Nat-option-result-err

Nat-option-result-err->get

Get the get field from a nat-option-result-err.

Signature
(nat-option-result-err->get x) → get
Arguments: x — Guard (nat-option-resultp x).
Returns: get — Type (fty::reserrp get).

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

Definitions and Theorems

Function: nat-option-result-err->get$inline

(defun nat-option-result-err->get$inline (x)
  (declare (xargs :guard (nat-option-resultp x)))
  (declare (xargs :guard (equal (nat-option-result-kind x)
                                :err)))
  (let ((__function__ 'nat-option-result-err->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (nat-option-result-kind x) :err)
                      x)))
           (fty::reserr-fix x))
         :exec x)))

Theorem: reserrp-of-nat-option-result-err->get

(defthm reserrp-of-nat-option-result-err->get
  (b* ((get (nat-option-result-err->get$inline x)))
    (fty::reserrp get))
  :rule-classes :rewrite)

Theorem: nat-option-result-err->get$inline-of-nat-option-result-fix-x

(defthm nat-option-result-err->get$inline-of-nat-option-result-fix-x
  (equal
       (nat-option-result-err->get$inline (nat-option-result-fix x))
       (nat-option-result-err->get$inline x)))

Theorem: nat-option-result-err->get$inline-nat-option-result-equiv-congruence-on-x

(defthm
 nat-option-result-err->get$inline-nat-option-result-equiv-congruence-on-x
 (implies (nat-option-result-equiv x x-equiv)
          (equal (nat-option-result-err->get$inline x)
                 (nat-option-result-err->get$inline x-equiv)))
 :rule-classes :congruence)

Theorem: nat-option-result-err->get-when-wrong-kind

(defthm nat-option-result-err->get-when-wrong-kind
  (implies (not (equal (nat-option-result-kind x) :err))
           (equal (nat-option-result-err->get x)
                  (fty::reserr-fix nil))))