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Proof-list-outcome-assertions

Proof-list-outcome-assertions->get

Get the get field from a proof-list-outcome-assertions.

Signature
(proof-list-outcome-assertions->get x) → get
Arguments: x — Guard (proof-list-outcomep x).
Returns: get — Type (assertion-listp get).

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

Definitions and Theorems

Function: proof-list-outcome-assertions->get$inline

(defun proof-list-outcome-assertions->get$inline (x)
  (declare (xargs :guard (proof-list-outcomep x)))
  (declare (xargs :guard (equal (proof-list-outcome-kind x)
                                :assertions)))
  (let ((__function__ 'proof-list-outcome-assertions->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (proof-list-outcome-kind x)
                             :assertions)
                      x)))
           (assertion-list-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: assertion-listp-of-proof-list-outcome-assertions->get

(defthm assertion-listp-of-proof-list-outcome-assertions->get
  (b* ((get (proof-list-outcome-assertions->get$inline x)))
    (assertion-listp get))
  :rule-classes :rewrite)

Theorem: proof-list-outcome-assertions->get$inline-of-proof-list-outcome-fix-x

(defthm
 proof-list-outcome-assertions->get$inline-of-proof-list-outcome-fix-x
 (equal (proof-list-outcome-assertions->get$inline
             (proof-list-outcome-fix x))
        (proof-list-outcome-assertions->get$inline x)))

Theorem: proof-list-outcome-assertions->get$inline-proof-list-outcome-equiv-congruence-on-x

(defthm
 proof-list-outcome-assertions->get$inline-proof-list-outcome-equiv-congruence-on-x
 (implies
      (proof-list-outcome-equiv x x-equiv)
      (equal (proof-list-outcome-assertions->get$inline x)
             (proof-list-outcome-assertions->get$inline x-equiv)))
 :rule-classes :congruence)

Theorem: proof-list-outcome-assertions->get-when-wrong-kind

(defthm proof-list-outcome-assertions->get-when-wrong-kind
  (implies (not (equal (proof-list-outcome-kind x)
                       :assertions))
           (equal (proof-list-outcome-assertions->get x)
                  (assertion-list-fix nil))))