void dispatchDependenciesChanged()

Notifies all dependent elements that this inherited widget has changed.

InheritedElement calls this function if InheritedWidget.updateShouldNotify returns true. Subclasses of InheritedElement might wish to call this function at other times if their inherited information changes outside of the build phase. InheritedWidget subclasses can also call this directly by first obtaining their InheritedElement using BuildContext.ancestorInheritedElementForWidgetOfExactType.

Source 

void dispatchDependenciesChanged() {
  for (Element dependent in _dependents) {
    assert(() {
      // check that it really is our descendant
      Element ancestor = dependent._parent;
      while (ancestor != this && ancestor != null)
        ancestor = ancestor._parent;
      return ancestor == this;
    });
    // check that it really deepends on us
    assert(dependent._dependencies.contains(this));
    dependent.dependenciesChanged();
  }
}