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Parser

Lex-repetition-1*-instruction

Lex 1*instruction.

Signature
(lex-repetition-1*-instruction 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*-instruction

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

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

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

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

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

Theorem: len-of-lex-repetition-1*-instruction-<=

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

Theorem: len-of-lex-repetition-1*-instruction-<

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

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

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

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

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