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





<b>assume </b><b>that </b><br/><a NAME="E1:53"/><i><font color="Green">E28</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>
 <b>and </b><br/><a NAME="E2:53"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E3:53"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E4:53"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">y</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D9" target="_self">Def9</a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:53_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">y</font></span>)</span>
 ;<br/><a NAME="E2:53_1"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T6" target="_self">Th6</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:53_1"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font>
 <b>by </b><i>, <a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:53"/>
<font color="Maroon">x</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">y</font> <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#D2" target="_self">Def2</a></i>;<br/>


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