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<b>let </b><font color="Maroon" title="c1">X</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">X0</font>, <font color="Olive" title="b2">X1</font>, <font color="Olive" title="b3">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Olive" title="b1">X0</font> &amp; <font color="Olive" title="b3">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Olive" title="b1">X0</font> holds <br/>for <font color="Olive" title="b4">Y1</font>, <font color="Olive" title="b5">Y2</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">X0</font>  st <font color="Olive" title="b4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b1">X0</font> &amp; <font color="Olive" title="b5">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b1">X0</font> &amp; <font color="Olive" title="b2">X1</font>,<font color="Olive" title="b3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  holds <br/><font color="Olive" title="b4">Y1</font>,<font color="Olive" title="b5">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> </span><br/><b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <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">X1</font>, <font color="Olive" title="b2">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Olive" title="b2">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> holds <br/>for <font color="Olive" title="b3">Y1</font>, <font color="Olive" title="b4">Y2</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X0</font>  st <font color="Olive" title="b3">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Olive" title="b4">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Olive" title="b1">X1</font>,<font color="Olive" title="b2">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  holds <br/><font color="Olive" title="b3">Y1</font>,<font color="Olive" title="b4">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> </span><br/><b>let </b><font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> implies for <font color="Olive" title="b1">Y1</font>, <font color="Olive" title="b2">Y2</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X0</font>  st <font color="Olive" title="b1">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Olive" title="b2">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  holds <br/><font color="Olive" title="b1">Y1</font>,<font color="Olive" title="b2">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>





<b>assume </b><a NAME="E1:46"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X0</font> )
 ; <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">Y1</font>, <font color="Olive" title="b2">Y2</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X0</font>  st <font color="Olive" title="b1">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Olive" title="b2">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  holds <br/><font color="Olive" title="b1">Y1</font>,<font color="Olive" title="b2">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> </span><br/>

<b>let </b><font color="Maroon" title="c5">Y1</font>, <font color="Maroon" title="c6">Y2</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c6">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  implies <font color="Maroon" title="c5">Y1</font>,<font color="Maroon" title="c6">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green" title="E31">A2</font></i>: 
( <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> &amp; <font color="Maroon" title="c6">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  or <font color="Maroon" title="c5">Y1</font>,<font color="Maroon" title="c6">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>

<b>assume </b><a NAME="E3:46"/>
<font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">Y1</font>,<font color="Maroon" title="c6">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> </span><br/>

<a NAME="E4:46"/><b>then </b>
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X0</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 
<b>by </b><i><a class="txt" href="#E1:46"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="tsep_1.html#T76" title="TSEP_1:th.76">TSEP_1:76</a></i>;<br/>
<b>hence </b><a NAME="E5:46"/>
<font color="Maroon" title="c5">Y1</font>,<font color="Maroon" title="c6">Y2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="tsep_2.html#T46" target="_self" title="TSEP_2:th.46">Th46</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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