Call method and reRender datatable on InputText change - jsf

Question

I'm learning some of JSF and I want know somethings. I already searched a lot in Google, Stack Overflow and famous websites like Mkyong and I didn't find the solution.
Actually I have one input text and a DataTable in the same page. The code appears something like this:
<h:form>
<h:inputText id="discipline"
value="#{disciplineMBean.name}"
valueChangeListener="#{disciplineMBean.updateList}">
<f:ajax event="keyup" reRender="myTable"/>
</h:inputText>
<h:commandButton value="Add" action="#{disciplineMBean.create}">
</h:commandButton>
</h:form>
<h:form>
<h:dataTable id="myTable" var="disciplina"
value="#{disciplinaMBean.disciplineList}">
<h:column>
<f:facet name="header">Name</f:facet>
<h:outputText value="#{discipline.name}" />
</h:column>
</h:dataTable>
</h:form>
What I want is: when the inputText value change, I want call the method "updateList", that will update the disciplineList with the matching disciplines (the connection with DB is ok). After that I want reRender "myTable" with the matched results - via Ajax, without page reload.
public void updateList(){
if( getName() != null && getName().length() > 0){
this.setDisciplineList( <working_connection_with_db_sending_getName()> );
}else{
this.setDisciplineList( <working_connection_with_db_all_results> );
}
}
Summarizing, I want that when user type something in input field, the disciplines list got updated with the matched disciplines - everything without page reload, when user change input field, the table is updated in real-time with the matching disciplines.
I can do something like that?
<h:inputText id="discipline" value="#{disciplineMBean.name}">
<f:ajax event="keyup" action="#{disciplineMBean.updateList}" reRender="myTable" />
</h:inputText>
Edit:
I already solved my problem, but I don't know if my way is the best way to do this things. So I will leave this question open and wait a answer explainning a better way to do this (for future users that need a similar feature). When a good answer be posted, I will give this the best answer.
Note: I translated the variable names, so sorry if I forget something.