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<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">PA</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PB</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PC</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">PA</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PC</font> &amp; <font color="Maroon">PB</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PC</font> )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PA</font> <a href="tarski.html#R1">c=</a>  <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PC</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:39"/><i><font color="Green">E45</font></i>: 
 <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PB</font> <a href="tarski.html#R1">c=</a>  <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PC</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:39"/><i><font color="Green">E48</font></i>: 
 <a href="partit1.html#K4" target="_self">ERl</a> <span class="p1">(<span class="default"><font color="Maroon">PA</font> <a href="partit1.html#K3" target="_self">'\/'</a> <font color="Maroon">PB</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PA</font></span>)</span> <a href="eqrel_1.html#K5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PB</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:39"/>
<span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PA</font></span>)</span> <a href="eqrel_1.html#K3">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PB</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PC</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
<span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PA</font></span>)</span> <a href="eqrel_1.html#K5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PB</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="partit1.html#K4" target="_self">ERl</a> <font color="Maroon">PC</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D3">EQREL_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon">PA</font> <a href="partit1.html#K3" target="_self">'\/'</a> <font color="Maroon">PB</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PC</font>
 <b>by </b><i>, </i>;<br/>


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