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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>) <b>-&gt; </b>  <a href="supinf_1.html#NM3">R_eal</a> =  <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<a NAME="E1:50_1_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:50_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<b>hence </b><a NAME="E2:50_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>) <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="supinf_2.html#T23" target="_self">Th23</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:50_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> st <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>)
 
<b>from </b><i><a class="ref" href="funct_2.html#S8">FUNCT_2:sch 8</a>(<a class="txt" href="supinf_2.html#E1:50_1_1"><i><font color="Green">E39</font></i></a>);<br/></i>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:50_1_1"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 ;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E5:50_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="supinf_2.html#E4:50_1_1"><i><font color="Green">E40</font></i></a></i>;<br/>


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