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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">PA</font>, <font color="Maroon" title="c3">PB</font>, <font color="Maroon" title="c4">PC</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E28">A1</font></i>: 
( <font color="Maroon" title="c2">PA</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c4">PC</font> &amp; <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c4">PC</font> )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green" title="E29">A2</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c4">PC</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T24" target="_self" title="PARTIT1:th.24">Th24</a></i>;<br/>
<a NAME="E3:39"/><i><font color="Green" title="E30">A3</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c3">PB</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c4">PC</font>
 
<b>by </b><i><a class="txt" href="partit1.html#E1:39"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="partit1.html#T24" target="_self" title="PARTIT1:th.24">Th24</a></i>;<br/>
<a NAME="E4:39"/><i><font color="Green" title="E31">A4</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">PA</font> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c3">PB</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c3">PB</font></span>)</span>
 
<b>by </b><i><a class="ref" href="partit1.html#T27" target="_self" title="PARTIT1:th.27">Th27</a></i>;<br/>
<a NAME="E5:39"/>
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c3">PB</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c4">PC</font>
 
<b>by </b><i><a class="txt" href="partit1.html#E2:39"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="partit1.html#E3:39"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c3">PB</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c4">PC</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon" title="c2">PA</font> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c4">PC</font>
 <b>by </b><i><a class="txt" href="partit1.html#E4:39"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="partit1.html#T24" target="_self" title="PARTIT1:th.24">Th24</a></i>;<br/>


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