<?xml version="1.0"?>
<div class="add">

<a NAME="E1:41_2_1"/>
 <a href="setfam_1.html#K2" title="SETFAM_1:func.2">UNION</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:41_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K2" title="SETFAM_1:func.2">UNION</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">X</font>, <font color="Maroon" title="c6">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:41_2_1_1"/><i><font color="Green" title="E20">A2</font></i>: 
( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c6">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">Y</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D4" title="SETFAM_1:def.4">SETFAM_1:def 4</a></i>;<br/>
<a NAME="E4:41_2_1_1"/>
<font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E3:41_2_1_1"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E5:41_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3:41_2_1_1"><i><font color="Green" title="E20">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:41_2_1"/>
 <a href="setfam_1.html#K2" title="SETFAM_1:func.2">UNION</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">T</font>
 ;<br/>


</div>
