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<b>let </b><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">K</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>;<br/>





<b>thus </b><a NAME="E1:21"/>
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">K</font>
 <b>by </b><i><a class="ref" href="substlat.html#T8" target="_self" title="SUBSTLAT:th.8">Th8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:21_1"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 ;<br/><a NAME="E2:21_1"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">a</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="substlat.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E3:21_1"/>
for <font color="Olive" title="b1">b</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b1">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">a</font> holds <br/><font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="substlat.html#E1:21_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="substlat.html#T5" target="_self" title="SUBSTLAT:th.5">Th5</a></i>;<br/><b>hence </b><a NAME="E4:21_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">K</font>
 <b>by </b><i><a class="txt" href="substlat.html#E1:21_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="substlat.html#E2:21_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="substlat.html#T7" target="_self" title="SUBSTLAT:th.7">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
<font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <font color="Maroon" title="c3">K</font>
 <b>by </b><i><a class="txt" href="substlat.html#E11"><i><font color="Green" title="E8">Lm2</font></i></a></i>;<br/>


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