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<b>let </b><font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c2">S</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>



<b>given </b><font color="Maroon" title="c3">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E2:16"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">S</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="wellord1.html#D8" title="WELLORD1:def.8">WELLORD1:def 8</a><br/>

<b>assume </b><a NAME="E3:16"/>
<font color="Maroon" title="c1">R</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">R</font> = <font color="Maroon" title="c1">R</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> ;<br/>
<a NAME="E5:16"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<a NAME="E6:16"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">F</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E2:16"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="wellord1.html#D7" title="WELLORD1:def.7">WELLORD1:def 7</a></i>;<br/>
<a NAME="E7:16"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">F</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T26" title="FINSET_1:th.26">FINSET_1:26</a></i>;<br/>
<a NAME="E8:16"/><b>then </b>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">S</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E2:16"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="wellord1.html#D7" title="WELLORD1:def.7">WELLORD1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E9:16"/>
<font color="Maroon" title="c2">S</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="orders_1.html#T196" title="ORDERS_1:th.196">ORDERS_1:196</a></i>;<br/>


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