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<b>let </b><font color="Maroon">F1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K3">Union</a> <font color="Maroon">X</font>, <a href="card_3.html#K3">Union</a> <font color="Maroon">D</font>, <font color="Maroon">F2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K3">Union</a> <font color="Maroon">X</font>, <a href="card_3.html#K3">Union</a> <font color="Maroon">D</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:10_1_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font><br/> 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> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <b>and </b><br/><a NAME="E2:10_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font><br/> 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> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/><font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><b>now </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="E1:10_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <font color="Maroon">X</font>
 ;<br/><b>then consider </b><font color="Maroon">i</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:10_1_2_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="card_5.html#T10">CARD_5:10</a></i>;<br/><b>reconsider </b><font color="Maroon">i</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> <b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>thus </b><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:10_1_2"/>
<font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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