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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>



<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E1:17"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="wellord1.html#R3">is_isomorphism_of</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="wellord1.html#D8">WELLORD1:def 8</a><br/>

<b>assume </b><a NAME="E2:17"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="relat_1.html#NM1">Relation</a> ;<br/>
<a NAME="E4:17"/>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<a NAME="E5:17"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E1:17"><i><font color="Green">E8</font></i></a>, <a class="ref" href="wellord1.html#D7">WELLORD1:def 7</a></i>;<br/>
<a NAME="E6:17"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T26">FINSET_1:26</a></i>;<br/>
<a NAME="E7:17"/><b>then </b>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E1:17"><i><font color="Green">E8</font></i></a>, <a class="ref" href="wellord1.html#D7">WELLORD1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E8:17"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="amistd_3.html#T3" target="_self">Th3</a></i>;<br/>


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