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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>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>







<a NAME="E1:28"/>
 <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>;<br/>
<a NAME="E2:28"/><b>then </b><i><font color="Green">E19</font></i>: 
<span class="p1">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="substlat.html#T14" target="_self">Th14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><a NAME="E2:28_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="substlat.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E3:28_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="txt" href="substlat.html#E1:28_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="substlat.html#E2"><i><font color="Green">Lemma1</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:28_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E6:28_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="substlat.html#E2:28_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="substlat.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/><b>thus </b><a NAME="E7:28_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="substlat.html#E2:28"><i><font color="Green">E19</font></i></a>, <a class="txt" href="substlat.html#E1:28_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="substlat.html#E5:28_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="substlat.html#E6:28_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="substlat.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:28"/>
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</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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