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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="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substlat.html#K1" target="_self">SubstitutionSet</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>thus </b><a NAME="E1:22"/>
 <a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="substlat.html#T8" target="_self">Th8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:22_1"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="txt" href="substlat.html#E2"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E3:22_1"/>
for <font color="Olive">b<sub>1</sub></font> being <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="substlat.html#E1:22_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="substlat.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E4:22_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="substlat.html#E1:22_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="substlat.html#E2:22_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="substlat.html#T7" target="_self">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:22"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="substlat.html#E11"><i><font color="Green">Lemma8</font></i></a></i>;<br/>


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