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Parser

Lex-repetition-3-operands

Lex 3( operand ws ).

Signature
(lex-repetition-3-operands 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-3-operands

(defun lex-repetition-3-operands (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-repetition-3-operands))
    (declare (ignorable __function__))
    (b* (((mv tree-operand-ws-1
              input-after-operand-ws-1)
          (lex-group-1-operand input))
         ((when (reserrp tree-operand-ws-1))
          (mv (reserrf-push tree-operand-ws-1)
              (nat-list-fix input)))
         ((mv tree-operand-ws-2
              input-after-operand-ws-2)
          (lex-group-1-operand input-after-operand-ws-1))
         ((when (reserrp tree-operand-ws-2))
          (mv (reserrf-push tree-operand-ws-2)
              (nat-list-fix input)))
         ((mv tree-operand-ws-3
              input-after-operand-ws-3)
          (lex-group-1-operand input-after-operand-ws-2))
         ((when (reserrp tree-operand-ws-3))
          (mv (reserrf-push tree-operand-ws-3)
              (nat-list-fix input))))
      (mv (list tree-operand-ws-1
                tree-operand-ws-2 tree-operand-ws-3)
          input-after-operand-ws-3))))

Theorem: tree-list-resultp-of-lex-repetition-3-operands.trees

(defthm tree-list-resultp-of-lex-repetition-3-operands.trees
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-3-operands input)))
    (abnf::tree-list-resultp trees))
  :rule-classes :rewrite)

Theorem: nat-listp-of-lex-repetition-3-operands.rest-input

(defthm nat-listp-of-lex-repetition-3-operands.rest-input
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-3-operands input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-lex-repetition-3-operands-<

(defthm len-of-lex-repetition-3-operands-<
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-3-operands input)))
    (implies (not (reserrp trees))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: lex-repetition-3-operands-of-nat-list-fix-input

(defthm lex-repetition-3-operands-of-nat-list-fix-input
  (equal (lex-repetition-3-operands (nat-list-fix input))
         (lex-repetition-3-operands input)))

Theorem: lex-repetition-3-operands-nat-list-equiv-congruence-on-input

(defthm lex-repetition-3-operands-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (lex-repetition-3-operands input)
                  (lex-repetition-3-operands input-equiv)))
  :rule-classes :congruence)