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Smtlink-hint

Smtlink-hint-fix

Fixing function for smtlink-hint structures.

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

Definitions and Theorems

Function: smtlink-hint-fix$inline

(defun smtlink-hint-fix$inline (x)
 (declare (xargs :guard (smtlink-hint-p x)))
 (let ((acl2::__function__ 'smtlink-hint-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (b* ((functions (func-list-fix (cdr (std::da-nth 0 x))))
        (hypotheses (hint-pair-list-fix (cdr (std::da-nth 1 x))))
        (main-hint (true-list-fix (cdr (std::da-nth 2 x))))
        (let-binding (let-binding-fix (cdr (std::da-nth 3 x))))
        (symbols (symbol-list-fix (cdr (std::da-nth 4 x))))
        (abs (symbol-list-fix (cdr (std::da-nth 5 x))))
        (fty (symbol-list-fix (cdr (std::da-nth 6 x))))
        (fty-info (fty-info-alist-fix (cdr (std::da-nth 7 x))))
        (fty-types (fty-types-fix (cdr (std::da-nth 8 x))))
        (int-to-rat (acl2::bool-fix (cdr (std::da-nth 9 x))))
        (smt-dir (str-fix (cdr (std::da-nth 10 x))))
        (rm-file (acl2::bool-fix (cdr (std::da-nth 11 x))))
        (smt-fname (str-fix (cdr (std::da-nth 12 x))))
        (smt-params (true-list-fix (cdr (std::da-nth 13 x))))
        (fast-functions (func-alist-fix (cdr (std::da-nth 14 x))))
        (type-decl-list (pseudo-term-fix (cdr (std::da-nth 15 x))))
        (expanded-clause-w/-hint
             (hint-pair-fix (cdr (std::da-nth 16 x))))
        (expanded-g/type (pseudo-term-fix (cdr (std::da-nth 17 x))))
        (smt-cnf (smtlink-config-fix (cdr (std::da-nth 18 x))))
        (wrld-fn-len (nfix (cdr (std::da-nth 19 x))))
        (custom-p (acl2::bool-fix (cdr (std::da-nth 20 x)))))
     (list (cons 'functions functions)
           (cons 'hypotheses hypotheses)
           (cons 'main-hint main-hint)
           (cons 'let-binding let-binding)
           (cons 'symbols symbols)
           (cons 'abs abs)
           (cons 'fty fty)
           (cons 'fty-info fty-info)
           (cons 'fty-types fty-types)
           (cons 'int-to-rat int-to-rat)
           (cons 'smt-dir smt-dir)
           (cons 'rm-file rm-file)
           (cons 'smt-fname smt-fname)
           (cons 'smt-params smt-params)
           (cons 'fast-functions fast-functions)
           (cons 'type-decl-list type-decl-list)
           (cons 'expanded-clause-w/-hint
                 expanded-clause-w/-hint)
           (cons 'expanded-g/type expanded-g/type)
           (cons 'smt-cnf smt-cnf)
           (cons 'wrld-fn-len wrld-fn-len)
           (cons 'custom-p custom-p)))
   :exec x)))

Theorem: smtlink-hint-p-of-smtlink-hint-fix

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

Theorem: smtlink-hint-fix-when-smtlink-hint-p

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

Function: smtlink-hint-equiv$inline

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

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

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

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

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

Theorem: smtlink-hint-fix-under-smtlink-hint-equiv

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

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

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

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

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

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

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

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

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