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<b>let </b><font color="Maroon">H1</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>, <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>, <font color="Maroon">H2</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>, <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:50_1_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> holds  <font color="Maroon">H1</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">x</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">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">x</font></span>)</span>
 <b>and </b><br/><a NAME="E2:50_1_2"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> holds  <font color="Maroon">H2</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">x</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">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Olive">x</font></span>)</span>
 ;<br/>

<a NAME="E3:50_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:50_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> ;<br/>
<font color="Maroon">H1</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font> = 
 <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T9" target="_self">Th9</a></i>
<br/>.= 
<font color="Maroon">H2</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="supinf_2.html#T10" target="_self">Th10</a></i>
;<br/>
<b>hence </b><a NAME="E4:50_1_2_1"/>
<font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:50_1_2"/>
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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