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

<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> is <a href="cohsp_1.html#V4" target="_self">union-distributive</a>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">X</font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>;<br/>
<b>assume </b><a NAME="E2:44"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> )
 ;<br/>

<a NAME="E3:44"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp;  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a>, <a class="ref" href="zfmisc_1.html#T93">ZFMISC_1:93</a></i>;<br/>
<b>hence </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font></span>)</span> = 
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="cohsp_1.html#D1" target="_self">Def1</a>, </i>
<br/>.= 
 <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="cohsp_1.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T118">FUNCT_1:118</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T93">ZFMISC_1:93</a></i>
;<br/><br/>


</div>
