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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</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>set </b><font color="Maroon">i</font> = <font color="Maroon">a</font>;<br/>
<b>assume </b><a NAME="E1:4"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:4"/><i><font color="Green">E49</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/>
<a NAME="E3:4"/><i><font color="Green">E51</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/>
<a NAME="E4:4"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:4_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/><b>thus </b><a NAME="E2:4_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i>, , , <a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:4_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:4_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1_1"><b>suppose </b></a><a NAME="E1:4_1_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">z</font>
<b>by </b><i>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , , , , <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1_2"><b>suppose </b></a><a NAME="E1:4_1_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:4"/>
<font color="Maroon">f</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">a</font>,<font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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