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



<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 ;<br/>

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:5"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:5"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E6:5"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E7:5"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:5"/><i><font color="Green">E45</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="E10:5"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E11:5"/>
( <font color="Maroon">x</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">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, , , , <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E12:5"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


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