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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>;<br/><b>let </b><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>assume </b><a NAME="E1:136"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">X1</font>,<font color="Maroon">X2</font> <a href="tsep_1.html#R4">are_weakly_separated</a> 
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/>

<a NAME="E2:136"/><i><font color="Green">E29</font></i>: 
( <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></i>;<br/>
<a NAME="E3:136"/><b>then </b><i><font color="Green">E35</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" target="_self">|</a> <font color="Maroon">X2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X2</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:136"/>
( <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <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> is  <a href="pre_topc.html#V5">continuous</a> <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> implies ( <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X1</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X1</font>,<font color="Maroon">Y</font> &amp; <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X2</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X2</font>,<font color="Maroon">Y</font> ) )
 <b>by </b><i>, <a class="txt" href="tmap_1.html#E12"><i><font color="Green">Lemma69</font></i></a></i>;<br/>

<b>thus </b><a NAME="E5:136"/>
( <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X1</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X1</font>,<font color="Maroon">Y</font> &amp; <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">X2</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X2</font>,<font color="Maroon">Y</font> implies <font color="Maroon">f</font> <a href="tmap_1.html#K2" target="_self">|</a> <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> is  <a href="pre_topc.html#V5">continuous</a> <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> )
 <b>by </b><i><a class="ref" href="tmap_1.html#T21" target="_self">Th21</a>, <a class="ref" href="tmap_1.html#T22" target="_self">Th22</a>, </i>;<br/>


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