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<b>let </b><font color="Maroon" title="c2">P</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">X</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">P</font> is <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a></span><br/>

<b>assume </b><a NAME="E1:46_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D9" title="SETFAM_1:def.9">SETFAM_1:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>hence </b><a NAME="E2:46_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="eqrel_1.html#D6" target="_self" title="EQREL_1:def.6">Def6</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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