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<b>let </b><font color="Maroon">F</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font>,<font color="Maroon">B</font>, <font color="Maroon">G</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font>,<font color="Maroon">B</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6_1_2"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 <b>and </b><br/><a NAME="E2:6_1_2"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">G</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">G</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">A0</font> = <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A0</font>;<br/><div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:6_1_2_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font>
 ;<br/><b>hence </b><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:6_1_2_1_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A2</font>
 ;<br/><b>hence </b><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:6_1_2_1"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:6_1_2"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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