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<b>let </b><font color="Maroon" title="c1">GX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B1</font>, <font color="Olive" title="b2">B2</font>, <font color="Olive" title="b3">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font> holds   <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">B2</font></span>)</span>,<font color="Olive" title="b3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Olive" title="b1">B1</font>,<font color="Olive" title="b3">V</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Olive" title="b2">B2</font>,<font color="Olive" title="b3">V</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</font>, <font color="Maroon" title="c4">V</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span>,<font color="Maroon" title="c4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c2">B1</font>,<font color="Maroon" title="c4">V</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c3">B2</font>,<font color="Maroon" title="c4">V</font></span>)</span></span><br/>



<a NAME="E1:4"/>
(  <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span>,<font color="Maroon" title="c4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">V</font> &amp;  <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c2">B1</font>,<font color="Maroon" title="c4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">V</font> &amp;  <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c3">B2</font>,<font color="Maroon" title="c4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">V</font> )
 
<b>by </b><i><a class="ref" href="connsp_3.html#D5" title="CONNSP_3:def.5">CONNSP_3:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:4"/>
 <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span>,<font color="Maroon" title="c4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c2">B1</font>,<font color="Maroon" title="c4">V</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> <font color="Maroon" title="c3">B2</font>,<font color="Maroon" title="c4">V</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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