<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">b1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font>, <font color="Maroon">b2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_2"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font> holds  <font color="Maroon">b1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="partfun1.html#K1">*</a> <font color="Olive">x</font>
 <b>and </b><br/><a NAME="E2:9_1_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font> holds  <font color="Maroon">b2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="partfun1.html#K1">*</a> <font color="Olive">x</font>
 ;<br/>

<a NAME="E3:9_1_2"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font> holds  <font color="Maroon">b1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font>, <font color="Maroon">y</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="autalg_1.html#K1" target="_self">UAAut</a> <font color="Maroon">UA</font>;<br/>

<b>thus </b><font color="Maroon">b1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> = 
<font color="Maroon">y</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:9_1_2"/>
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


</div>
