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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>, <font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span>,<font color="Maroon">Y</font>;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="146_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:146_1"/>
<font color="Maroon">X1</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font>
 ;<br/><a NAME="E2:146_1"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> &amp; <font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X2</font> &amp; <font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X2</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> )
 <b>by </b><i><a class="ref" href="tsep_1.html#T22">TSEP_1:22</a>, <a class="ref" href="tsep_1.html#T30">TSEP_1:30</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X1</font></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font></span>)</span> = 
<font color="Maroon">g</font> <a href="tmap_1.html#K3" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font></span>)</span>
<b>by </b><i><a class="ref" href="tmap_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X2</font></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font></span>)</span>
<b>by </b><i><a class="ref" href="tmap_1.html#T31" target="_self">Th31</a>, <a class="ref" href="tmap_1.html#T6" target="_self">Th6</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:146"/>
<font color="Maroon">g</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X1</font></span>)</span> <a href="tmap_1.html#K10" target="_self">union</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X2</font></span>)</span>
 <b>by </b><i><a class="ref" href="tmap_1.html#T27" target="_self">Th27</a></i>;<br/>


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