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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>;<br/><b>let </b><font color="Maroon" title="c4">X1</font>, <font color="Maroon" title="c5">X2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:135"/><i><font color="Green" title="E99">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X2</font>
 <b>and </b><br/><a NAME="E2:135"/><i><font color="Green" title="E100">A2</font></i>: 
<font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c5">X2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a> 
 ;<br/>

<b>thus </b><a NAME="E3:135"/>
( <font color="Maroon" title="c3">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> implies ( <font color="Maroon" title="c3">f</font> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <font color="Maroon" title="c4">X1</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">f</font> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <font color="Maroon" title="c5">X2</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X2</font>,<font color="Maroon" title="c2">Y</font> ) )
 <b>by </b><i><a class="ref" href="tmap_1.html#T68" target="_self" title="TMAP_1:th.68">Th68</a></i>;<br/>

<b>assume </b><a NAME="E4:135"/>
( <font color="Maroon" title="c3">f</font> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <font color="Maroon" title="c4">X1</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">f</font> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <font color="Maroon" title="c5">X2</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X2</font>,<font color="Maroon" title="c2">Y</font> )
 ;<br/>

<a NAME="E5:135"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X2</font></span>)</span> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X2</font></span>)</span>,<font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E2:135"><i><font color="Green" title="E100">A2</font></i></a>, <a class="ref" href="tmap_1.html#T129" target="_self" title="TMAP_1:th.129">Th129</a></i>;<br/>
<b>hence </b><a NAME="E6:135"/>
<font color="Maroon" title="c3">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:135"><i><font color="Green" title="E99">A1</font></i></a>, <a class="ref" href="tmap_1.html#T60" target="_self" title="TMAP_1:th.60">Th60</a></i>;<br/>


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