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Output-expression

Output-expression-fix

Fixing function for output-expression structures.

Signature
(output-expression-fix x) → new-x
Arguments: x — Guard (output-expressionp x).
Returns: new-x — Type (output-expressionp new-x).

Definitions and Theorems

Function: output-expression-fix$inline

(defun output-expression-fix$inline (x)
  (declare (xargs :guard (output-expressionp x)))
  (let ((__function__ 'output-expression-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((get (expression-fix (cdr (std::da-nth 0 (cdr x))))))
           (cons :output-expression (list (cons 'get get))))
         :exec x)))

Theorem: output-expressionp-of-output-expression-fix

(defthm output-expressionp-of-output-expression-fix
  (b* ((new-x (output-expression-fix$inline x)))
    (output-expressionp new-x))
  :rule-classes :rewrite)

Theorem: output-expression-fix-when-output-expressionp

(defthm output-expression-fix-when-output-expressionp
  (implies (output-expressionp x)
           (equal (output-expression-fix x) x)))

Function: output-expression-equiv$inline

(defun output-expression-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (output-expressionp acl2::x)
                              (output-expressionp acl2::y))))
  (equal (output-expression-fix acl2::x)
         (output-expression-fix acl2::y)))

Theorem: output-expression-equiv-is-an-equivalence

(defthm output-expression-equiv-is-an-equivalence
  (and (booleanp (output-expression-equiv x y))
       (output-expression-equiv x x)
       (implies (output-expression-equiv x y)
                (output-expression-equiv y x))
       (implies (and (output-expression-equiv x y)
                     (output-expression-equiv y z))
                (output-expression-equiv x z)))
  :rule-classes (:equivalence))

Theorem: output-expression-equiv-implies-equal-output-expression-fix-1

(defthm
      output-expression-equiv-implies-equal-output-expression-fix-1
  (implies (output-expression-equiv acl2::x x-equiv)
           (equal (output-expression-fix acl2::x)
                  (output-expression-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: output-expression-fix-under-output-expression-equiv

(defthm output-expression-fix-under-output-expression-equiv
  (output-expression-equiv (output-expression-fix acl2::x)
                           acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-output-expression-fix-1-forward-to-output-expression-equiv

(defthm
 equal-of-output-expression-fix-1-forward-to-output-expression-equiv
 (implies (equal (output-expression-fix acl2::x)
                 acl2::y)
          (output-expression-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-output-expression-fix-2-forward-to-output-expression-equiv

(defthm
 equal-of-output-expression-fix-2-forward-to-output-expression-equiv
 (implies (equal acl2::x (output-expression-fix acl2::y))
          (output-expression-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: output-expression-equiv-of-output-expression-fix-1-forward

(defthm output-expression-equiv-of-output-expression-fix-1-forward
  (implies (output-expression-equiv (output-expression-fix acl2::x)
                                    acl2::y)
           (output-expression-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: output-expression-equiv-of-output-expression-fix-2-forward

(defthm output-expression-equiv-of-output-expression-fix-2-forward
 (implies
   (output-expression-equiv acl2::x (output-expression-fix acl2::y))
   (output-expression-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)