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Parser

Lex-repetition-1*-tuple

Lex 1*tuple.

Signature
(lex-repetition-1*-tuple input) → (mv trees rest-input)
Arguments: input — Guard (nat-listp input).
Returns: trees — Type (abnf::tree-list-resultp trees).; rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: lex-repetition-1*-tuple

(defun lex-repetition-1*-tuple (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-repetition-1*-tuple))
    (declare (ignorable __function__))
    (b* (((mv tree-1-tuple input-after-1)
          (lex-tuple input))
         ((when (reserrp tree-1-tuple))
          (mv tree-1-tuple (nat-list-fix input)))
         ((mv trees-rest-tuple input-after-rest)
          (lex-repetition-*-tuple input-after-1))
         ((when (reserrp trees-rest-tuple))
          (mv (reserrf "1*tuple problem")
              (nat-list-fix input))))
      (mv (cons tree-1-tuple trees-rest-tuple)
          input-after-rest))))

Theorem: tree-list-resultp-of-lex-repetition-1*-tuple.trees

(defthm tree-list-resultp-of-lex-repetition-1*-tuple.trees
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-1*-tuple input)))
    (abnf::tree-list-resultp trees))
  :rule-classes :rewrite)

Theorem: nat-listp-of-lex-repetition-1*-tuple.rest-input

(defthm nat-listp-of-lex-repetition-1*-tuple.rest-input
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-1*-tuple input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-lex-1*-tuple-<

(defthm len-of-lex-1*-tuple-<
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-1*-tuple input)))
    (implies (not (reserrp trees))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: lex-repetition-1*-tuple-of-nat-list-fix-input

(defthm lex-repetition-1*-tuple-of-nat-list-fix-input
  (equal (lex-repetition-1*-tuple (nat-list-fix input))
         (lex-repetition-1*-tuple input)))

Theorem: lex-repetition-1*-tuple-nat-list-equiv-congruence-on-input

(defthm lex-repetition-1*-tuple-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (lex-repetition-1*-tuple input)
                  (lex-repetition-1*-tuple input-equiv)))
  :rule-classes :congruence)