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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">A2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">g2</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A2</font>,<font color="Maroon">B</font>;<br/>













<b>assume </b><a NAME="E1:8"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g1</font> &amp; <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> )
 ;<br/>

<a NAME="E2:8"/>
( <font color="Maroon">A1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f1</font> = <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font>,<font color="Maroon">B</font> <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<a NAME="E4:8"/>
( <font color="Maroon">A2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f2</font> = <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A2</font>,<font color="Maroon">B</font> <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<a NAME="E6:8"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>then </b><font color="Maroon">f1</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span> = 
<font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T82">FUNCT_1:82</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T82">FUNCT_1:82</a></i>
;<br/>
<b>hence </b><a NAME="E8:8"/>
<font color="Maroon">g</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g1</font> <a href="tmap_1.html#K1" target="_self">union</a> <font color="Maroon">g2</font>
 <b>by </b><i>, </i>;<br/>


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