Classes you need to love, the sooner the better!
One option for what you want may look like this:
import sys
import threading
from PyQt5 import QtWidgets, QtCore   # ,uic 
def thread(my_func):
    """  Runs a function in a separate thread. """
    def wrapper(*args, **kwargs):
        my_thread = threading.Thread(target=my_func, args=args, kwargs=kwargs)
        my_thread.start()
    return wrapper
@thread
def processing(signal):
    """ Emulates the processing of some data. """
    ind = 1
    for i in range (1,10001):                                     # +++
        html = ("<p style='color:blue;'> Completed: <b>%s </b> </p> <br>") % i
        QtCore.QThread.msleep(5)
        ind = ind if i%100!=0 else ind+1                          # +++
        signal.emit(html, ind)                                    # +++ 
def mySignalHandler(html, val):          # Called to process a signal
    plainTextEdit.appendHtml(html)
    progressBar.setValue(val)
class WindowSignal(QtWidgets.QWidget):
    """ New signals can be defined as class attributes using the pyqtSignal() factory. """
    my_signal = QtCore.pyqtSignal(str, int, name='my_signal')
if __name__ == '__main__':
    app = QtWidgets.QApplication(sys.argv)
    window = WindowSignal()
    button = QtWidgets.QPushButton("Emit your signal!", window)
    button.clicked.connect(lambda: processing(window.my_signal))
    # since you do not publish test.ui, I replaced it with the line below:
    plainTextEdit = QtWidgets.QPlainTextEdit(window)
    progressBar = QtWidgets.QProgressBar()
    progressBar.setTextVisible(False)
    layoutHBox = QtWidgets.QHBoxLayout()
    layoutHBox.addWidget(button)
    layoutHBox.addWidget(plainTextEdit)
    layoutVBox = QtWidgets.QVBoxLayout()
    window.setLayout(layoutVBox)
    layoutVBox.addLayout(layoutHBox)
    layoutVBox.addWidget(progressBar)
    window.my_signal.connect(mySignalHandler, QtCore.Qt.QueuedConnection)
    window.show()
    sys.exit(app.exec_())

Example 2:
test.ui is a file containing the description of the main window automatically generated by Qt Designer.
<?xml version="1.0" encoding="UTF-8"?>
<ui version="4.0">
 <class>Form</class>
 <widget class="QWidget" name="Form">
  <property name="geometry">
   <rect>
    <x>0</x>
    <y>0</y>
    <width>400</width>
    <height>300</height>
   </rect>
  </property>
  <property name="windowTitle">
   <string>Form</string>
  </property>
  <widget class="QWidget" name="">
   <property name="geometry">
    <rect>
     <x>12</x>
     <y>12</y>
     <width>371</width>
     <height>281</height>
    </rect>
   </property>
   <layout class="QVBoxLayout" name="verticalLayout">
    <item>
     <layout class="QHBoxLayout" name="horizontalLayout">
      <item>
       <widget class="QPushButton" name="button">
        <property name="text">
         <string>Emit your signal!</string>
        </property>
       </widget>
      </item>
      <item>
       <widget class="QPlainTextEdit" name="plainTextEdit"/>
      </item>
     </layout>
    </item>
    <item>
     <widget class="QProgressBar" name="progressBar">
      <property name="value">
       <number>0</number>
      </property>
      <property name="textVisible">
       <bool>false</bool>
      </property>
      <property name="invertedAppearance">
       <bool>false</bool>
      </property>
     </widget>
    </item>
   </layout>
  </widget>
 </widget>
 <resources/>
 <connections/>
</ui>
main.py
import sys
import threading
from PyQt5 import QtWidgets, QtCore, uic 
def thread(my_func):
    """  Runs a function in a separate thread. """
    def wrapper(*args, **kwargs):
        my_thread = threading.Thread(target=my_func, args=args, kwargs=kwargs)
        my_thread.start()
    return wrapper
@thread
def processing(signal):
    """ Emulates the processing of some data. """
    for i in range (1,101):   # (1,100000)
        html = ("<p style='color:blue;'> Completed: <b>%s </b> </p> <br>") % i
        QtCore.QThread.msleep(10)
        signal.emit(html, i)     # Send a signal in which we transfer the received data
def mySignalHandler(html, val):          # Called to process a signal
    window.plainTextEdit.appendHtml(html)
    window.progressBar.setValue(val)
class WindowSignal(QtWidgets.QWidget):
    """ New signals can be defined as class attributes using the pyqtSignal() factory. """
    my_signal = QtCore.pyqtSignal(str, int, name='my_signal')
if __name__ == '__main__':
    app = QtWidgets.QApplication(sys.argv)
    window = WindowSignal()
    uic.loadUi('test.ui', window)    
    window.button.clicked.connect(lambda: processing(window.my_signal))
    window.my_signal.connect(mySignalHandler, QtCore.Qt.QueuedConnection)
    window.show()
    sys.exit(app.exec_())
