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Parser

Lex-repetition-1*-program-declaration

Lex 1*( mapping / struct / record / function / transition ).

Signature
(lex-repetition-1*-program-declaration 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*-program-declaration

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

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

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

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

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

Theorem: len-of-lex-repetition-1*-program-declaration-<=

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

Theorem: len-of-lex-repetition-1*-program-declaration-<

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

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

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

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

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