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    • Dead-code-eliminator-execution

    Funenv-result-dead

    Eliminate dead code in errors and function environments.

    Signature
    (funenv-result-dead funenv?) → new-funenv?
    Arguments
    funenv? — Guard (funenv-resultp funenv?).
    Returns
    new-funenv? — Type (funenv-resultp new-funenv?).

    We transform function environments and leave errors unchanged.

    Definitions and Theorems

    Function: funenv-result-dead

    (defun funenv-result-dead (funenv?)
      (declare (xargs :guard (funenv-resultp funenv?)))
      (let ((__function__ 'funenv-result-dead))
        (declare (ignorable __function__))
        (b* ((funenv? (funenv-result-fix funenv?)))
          (if (reserrp funenv?)
              funenv?
            (funenv-dead funenv?)))))

    Theorem: funenv-resultp-of-funenv-result-dead

    (defthm funenv-resultp-of-funenv-result-dead
      (b* ((new-funenv? (funenv-result-dead funenv?)))
        (funenv-resultp new-funenv?))
      :rule-classes :rewrite)

    Theorem: funenv-result-dead-of-funenv-result-fix-funenv?

    (defthm funenv-result-dead-of-funenv-result-fix-funenv?
      (equal (funenv-result-dead (funenv-result-fix funenv?))
             (funenv-result-dead funenv?)))

    Theorem: funenv-result-dead-funenv-result-equiv-congruence-on-funenv?

    (defthm funenv-result-dead-funenv-result-equiv-congruence-on-funenv?
      (implies (funenv-result-equiv funenv? funenv?-equiv)
               (equal (funenv-result-dead funenv?)
                      (funenv-result-dead funenv?-equiv)))
      :rule-classes :congruence)