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<a NAME="E1:1_1_1"/><i><font color="Green">E16</font></i>: 
 <a href="partit1.html#K1">PARTITIONS</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="partit1.html#K1">PARTITIONS</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> is    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D3">PARTIT1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:1_1_1"/>
for <font color="Olive">S</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">S</font> <a href="hidden.html#R2">in</a>  <a href="partit1.html#K1">PARTITIONS</a> <font color="Maroon">X</font> holds <br/><font color="Olive">S</font> is    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D3">PARTIT1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:1_1_1"/>
 <a href="partit1.html#K1">PARTITIONS</a> <font color="Maroon">X</font> is   <a href="t_1topsp.html#NM2">Part-Family</a> of <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="t_1topsp.html#D2">T_1TOPSP:def 2</a>, <a class="ref" href="t_1topsp.html#D3">T_1TOPSP:def 3</a></i>;<br/>


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