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Outcome-proof-obligation-failure

Outcome-proof-obligation-failure->obligation-expr

Get the obligation-expr field from a outcome-proof-obligation-failure.

Signature
(outcome-proof-obligation-failure->obligation-expr x) → obligation-expr
Arguments: x — Guard (outcomep x).
Returns: obligation-expr — Type (expressionp obligation-expr).

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

Definitions and Theorems

Function: outcome-proof-obligation-failure->obligation-expr$inline

(defun outcome-proof-obligation-failure->obligation-expr$inline (x)
  (declare (xargs :guard (outcomep x)))
  (declare (xargs :guard (equal (outcome-kind x)
                                :proof-obligation-failure)))
  (let ((__function__
             'outcome-proof-obligation-failure->obligation-expr))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (outcome-kind x)
                             :proof-obligation-failure)
                      x)))
           (expression-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: expressionp-of-outcome-proof-obligation-failure->obligation-expr

(defthm
   expressionp-of-outcome-proof-obligation-failure->obligation-expr
 (b*
  ((obligation-expr
      (outcome-proof-obligation-failure->obligation-expr$inline x)))
  (expressionp obligation-expr))
 :rule-classes :rewrite)

Theorem: outcome-proof-obligation-failure->obligation-expr$inline-of-outcome-fix-x

(defthm
 outcome-proof-obligation-failure->obligation-expr$inline-of-outcome-fix-x
 (equal
      (outcome-proof-obligation-failure->obligation-expr$inline
           (outcome-fix x))
      (outcome-proof-obligation-failure->obligation-expr$inline x)))

Theorem: outcome-proof-obligation-failure->obligation-expr$inline-outcome-equiv-congruence-on-x

(defthm
 outcome-proof-obligation-failure->obligation-expr$inline-outcome-equiv-congruence-on-x
 (implies
   (outcome-equiv x x-equiv)
   (equal
        (outcome-proof-obligation-failure->obligation-expr$inline x)
        (outcome-proof-obligation-failure->obligation-expr$inline
             x-equiv)))
 :rule-classes :congruence)

Theorem: outcome-proof-obligation-failure->obligation-expr-when-wrong-kind

(defthm
  outcome-proof-obligation-failure->obligation-expr-when-wrong-kind
  (implies
       (not (equal (outcome-kind x)
                   :proof-obligation-failure))
       (equal (outcome-proof-obligation-failure->obligation-expr x)
              (expression-fix nil))))