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<b>let </b><font color="Maroon">b1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>, <font color="Maroon">b2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7_1_2"/><i><font color="Green">E89</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">x1</font>, <font color="Olive">y1</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font> &amp; <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Olive">x</font> &amp; <font color="Olive">y1</font> <a href="hidden.html#R2">in</a> <font color="Olive">y</font> holds <br/><font color="Maroon">b1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <font color="Olive">x1</font>,<font color="Olive">y1</font></span>)</span>
 <b>and </b><br/><a NAME="E2:7_1_2"/><i><font color="Green">E90</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">x1</font>, <font color="Olive">y1</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font> &amp; <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Olive">x</font> &amp; <font color="Olive">y1</font> <a href="hidden.html#R2">in</a> <font color="Olive">y</font> holds <br/><font color="Maroon">b2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <font color="Olive">x1</font>,<font color="Olive">y1</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:7_1_2_1"/><i><font color="Green">E91</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:7_1_2_1"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Maroon">y1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><a NAME="E5:7_1_2_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> )
 <b>by </b><i>, , <a class="ref" href="eqrel_1.html#T28">EQREL_1:28</a></i>;<br/><a NAME="E6:7_1_2_1"/><b>then </b>
( <font color="Maroon">b1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span> &amp; <font color="Maroon">b2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E7:7_1_2_1"/>
<font color="Maroon">b1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_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/>


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