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• Smtlink-hint-syntax

Smtlink-hint-syntax-p-helper

Helper function for smtlink-hint-syntax-p.

Signature

(smtlink-hint-syntax-p-helper term used) → syntax-good?

Arguments

used — Guard (smtlink-option-name-lst-p used).

Returns

syntax-good? — Type (booleanp syntax-good?).

Definitions and Theorems

Function: smtlink-hint-syntax-p-helper

(defun smtlink-hint-syntax-p-helper (term used)
  (declare (xargs :guard (smtlink-option-name-lst-p used)))
  (let ((acl2::__function__ 'smtlink-hint-syntax-p-helper))
    (declare (ignorable acl2::__function__))
    (b* (((unless (true-listp term)) nil)
         ((if (atom term)) (equal term nil))
         ((unless (cdr term)) nil)
         ((list* first second rest) term)
         ((mv res new-used)
          (smtlink-option-syntax-p (list first second)
                                   used)))
      (and res
           (smtlink-hint-syntax-p-helper rest new-used)))))

Theorem: booleanp-of-smtlink-hint-syntax-p-helper

(defthm booleanp-of-smtlink-hint-syntax-p-helper
  (b* ((syntax-good? (smtlink-hint-syntax-p-helper term used)))
    (booleanp syntax-good?))
  :rule-classes :rewrite)

Theorem: smtlink-hint-syntax-p-helper--monotonicity

(defthm smtlink-hint-syntax-p-helper--monotonicity
  (implies (and (subsetp used-1 used :test 'equal)
                (smtlink-hint-syntax-p-helper term used))
           (smtlink-hint-syntax-p-helper term used-1)))

Theorem: smtlink-hint-syntax-p-helper--congruence

(defthm smtlink-hint-syntax-p-helper--congruence
  (b* ((ok (smtlink-hint-syntax-p-helper term used)))
    (implies (acl2::set-equiv used-1 used)
             (equal (smtlink-hint-syntax-p-helper term used-1)
                    ok)))
  :rule-classes (:congruence))

Theorem: smtlink-hint-syntax-p-helper-preserve

(defthm smtlink-hint-syntax-p-helper-preserve
  (implies (and (smtlink-hint-syntax-p-helper term nil)
                (consp term))
           (smtlink-hint-syntax-p-helper (cddr term)
                                         nil)))