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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))))