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Smtlink-config

Smtlink-config-fix

Fixing function for smtlink-config structures.

Signature
(smtlink-config-fix x) → new-x
Arguments: x — Guard (smtlink-config-p x).
Returns: new-x — Type (smtlink-config-p new-x).

Definitions and Theorems

Function: smtlink-config-fix$inline

(defun smtlink-config-fix$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (let ((acl2::__function__ 'smtlink-config-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((interface-dir (str-fix (cdr (std::da-nth 0 x))))
              (smt-module (str-fix (cdr (std::da-nth 1 x))))
              (smt-class (str-fix (cdr (std::da-nth 2 x))))
              (smt-cmd (str-fix (cdr (std::da-nth 3 x))))
              (pythonpath (str-fix (cdr (std::da-nth 4 x)))))
           (list (cons 'interface-dir interface-dir)
                 (cons 'smt-module smt-module)
                 (cons 'smt-class smt-class)
                 (cons 'smt-cmd smt-cmd)
                 (cons 'pythonpath pythonpath)))
         :exec x)))

Theorem: smtlink-config-p-of-smtlink-config-fix

(defthm smtlink-config-p-of-smtlink-config-fix
  (b* ((new-x (smtlink-config-fix$inline x)))
    (smtlink-config-p new-x))
  :rule-classes :rewrite)

Theorem: smtlink-config-fix-when-smtlink-config-p

(defthm smtlink-config-fix-when-smtlink-config-p
  (implies (smtlink-config-p x)
           (equal (smtlink-config-fix x) x)))

Function: smtlink-config-equiv$inline

(defun smtlink-config-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (smtlink-config-p acl2::x)
                              (smtlink-config-p acl2::y))))
  (equal (smtlink-config-fix acl2::x)
         (smtlink-config-fix acl2::y)))

Theorem: smtlink-config-equiv-is-an-equivalence

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

Theorem: smtlink-config-equiv-implies-equal-smtlink-config-fix-1

(defthm smtlink-config-equiv-implies-equal-smtlink-config-fix-1
  (implies (smtlink-config-equiv acl2::x x-equiv)
           (equal (smtlink-config-fix acl2::x)
                  (smtlink-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: smtlink-config-fix-under-smtlink-config-equiv

(defthm smtlink-config-fix-under-smtlink-config-equiv
  (smtlink-config-equiv (smtlink-config-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-smtlink-config-fix-1-forward-to-smtlink-config-equiv

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

Theorem: equal-of-smtlink-config-fix-2-forward-to-smtlink-config-equiv

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

Theorem: smtlink-config-equiv-of-smtlink-config-fix-1-forward

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

Theorem: smtlink-config-equiv-of-smtlink-config-fix-2-forward

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