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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">PA</font>, <font color="Olive" title="b2">PB</font>, <font color="Olive" title="b3">PC</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">PA</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Olive" title="b3">PC</font> &amp; <font color="Olive" title="b2">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Olive" title="b3">PC</font> holds <br/><font color="Olive" title="b1">PA</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Olive" title="b2">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Olive" title="b3">PC</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">PA</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font> &amp; <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font> implies <font color="Maroon" title="c2">PA</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font> )</span><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#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font> &amp; <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">PA</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c4">PC</font></span><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="c4">PC</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="c2">PA</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="c4">PC</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="c3">PB</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"/>
 <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#K2" title="PARTIT1:func.2">'/\'</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#K4" title="EQREL_1:func.4">/\</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#T28" target="_self" title="PARTIT1:th.28">Th28</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c4">PC</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <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#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c3">PB</font></span>)</span>
 
<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#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon" title="c2">PA</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c3">PB</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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