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Proof-outcome-assertion

Proof-outcome-assertion->get

Get the get field from a proof-outcome-assertion.

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

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

Definitions and Theorems

Function: proof-outcome-assertion->get$inline

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

Theorem: assertionp-of-proof-outcome-assertion->get

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

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

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

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

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

Theorem: proof-outcome-assertion->get-when-wrong-kind

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