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Parser

Lex-repetition-1-digit--underbar

Lex 1*( digit *"_".

Signature
(lex-repetition-1*-digit-*-underbar 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*-digit-*-underbar

(defun lex-repetition-1*-digit-*-underbar (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-repetition-1*-digit-*-underbar))
    (declare (ignorable __function__))
    (b* (((mv tree-thing1 input-after-thing1)
          (lex-group-digit-*-underbar input))
         ((when (reserrp tree-thing1))
          (mv (reserrf-push tree-thing1)
              (nat-list-fix input)))
         ((mv trees input-after-trees)
          (lex-repetition-*-digit-*-underbar input-after-thing1)))
      (mv (cons tree-thing1 trees)
          input-after-trees))))

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

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

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

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

Theorem: len-of-lex-repetition-1*-digit-*-underbar-<=

(defthm len-of-lex-repetition-1*-digit-*-underbar-<=
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-1*-digit-*-underbar input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-lex-repetition-1*-digit-*-underbar-<

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

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

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

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

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

Lex-repetition-1*-digit-*-underbar

Definitions and Theorems

Lex-repetition-1-digit--underbar