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    • Proof-tree-equal

    Proof-tree-equal->asg

    Get the asg field from a proof-tree-equal.

    Signature
    (proof-tree-equal->asg x) → asg
    Arguments
    x — Guard (proof-treep x).
    Returns
    asg — Type (assignmentp asg).

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

    Definitions and Theorems

    Function: proof-tree-equal->asg$inline

    (defun proof-tree-equal->asg$inline (x)
      (declare (xargs :guard (proof-treep x)))
      (declare (xargs :guard (equal (proof-tree-kind x) :equal)))
      (let ((__function__ 'proof-tree-equal->asg))
        (declare (ignorable __function__))
        (mbe :logic
             (b* ((x (and (equal (proof-tree-kind x) :equal)
                          x)))
               (assignment-fix (std::da-nth 0 (cdr x))))
             :exec (std::da-nth 0 (cdr x)))))

    Theorem: assignmentp-of-proof-tree-equal->asg

    (defthm assignmentp-of-proof-tree-equal->asg
      (b* ((asg (proof-tree-equal->asg$inline x)))
        (assignmentp asg))
      :rule-classes :rewrite)

    Theorem: proof-tree-equal->asg$inline-of-proof-tree-fix-x

    (defthm proof-tree-equal->asg$inline-of-proof-tree-fix-x
      (equal (proof-tree-equal->asg$inline (proof-tree-fix x))
             (proof-tree-equal->asg$inline x)))

    Theorem: proof-tree-equal->asg$inline-proof-tree-equiv-congruence-on-x

    (defthm
          proof-tree-equal->asg$inline-proof-tree-equiv-congruence-on-x
      (implies (proof-tree-equiv x x-equiv)
               (equal (proof-tree-equal->asg$inline x)
                      (proof-tree-equal->asg$inline x-equiv)))
      :rule-classes :congruence)

    Theorem: proof-tree-equal->asg-when-wrong-kind

    (defthm proof-tree-equal->asg-when-wrong-kind
      (implies (not (equal (proof-tree-kind x) :equal))
               (equal (proof-tree-equal->asg x)
                      (assignment-fix nil))))