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<b>let </b><font color="Maroon">F</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">i1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">i2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">xi1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Ai2</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">i2</font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E3:6"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="pralg_3.html#D2">PRALG_3:def 2</a></i>;<br/>
<b>assume </b><a NAME="E4:6"/>
<font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i1</font>,<font color="Maroon">xi1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span> <a href="relat_1.html#K10">"</a> <font color="Maroon">Ai2</font>
 ;<br/>

<a NAME="E5:6"/><b>then </b>
( <font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i1</font>,<font color="Maroon">xi1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i1</font>,<font color="Maroon">xi1</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">Ai2</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E6:6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i1</font>,<font color="Maroon">xi1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Ai2</font>
 
<b>by </b><i><a class="ref" href="pralg_3.html#D2">PRALG_3:def 2</a></i>;<br/>
<a NAME="E7:6"/><b>then </b>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Ai2</font>
 
<b>by </b><i>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/>
<a NAME="E8:6"/><b>then </b>
<span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Ai2</font>
 
<b>by </b><i>, <a class="ref" href="pralg_3.html#D2">PRALG_3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E9:6"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3">proj</a> <font color="Maroon">F</font>,<font color="Maroon">i2</font></span>)</span> <a href="relat_1.html#K10">"</a> <font color="Maroon">Ai2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


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