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





<b>assume </b><a NAME="E1:60"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span>
 ;<br/>

<b>take </b>
<font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span>
;<br/>

<b>take </b>
<font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
;<br/>

<a NAME="E2:60"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_1.html#E2:60"><i><font color="Green">E34</font></i></a>, </i>;<br/>
<a NAME="E3:60"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T25">FUNCT_4:25</a></i>;<br/>
<a NAME="E4:60"/><b>then </b>
 <a href="ami_1.html#K7" target="_self">sproduct</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:60"/>
<font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D10" target="_self">Def10</a></i>;<br/>

<a NAME="E6:60"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T24">FUNCT_4:24</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:60"><i><font color="Green">E34</font></i></a>, </i>;<br/>

<a NAME="E8:60"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_1.html#E2:60"><i><font color="Green">E34</font></i></a>, </i>;<br/>
<a NAME="E9:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E10:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>;<br/>
<b>hence </b><a NAME="E11:60"/>
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T74">FUNCT_4:74</a></i>;<br/>


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