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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font>, <font color="Olive" title="b3">Y1</font>, <font color="Olive" title="b4">Y2</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>,<font color="Olive" title="b3">Y1</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  &amp; <font color="Olive" title="b2">X2</font>,<font color="Olive" title="b4">Y2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  &amp; <font color="Olive" title="b3">Y1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Olive" title="b4">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) &amp; <font color="Olive" title="b3">Y1</font>,<font color="Olive" title="b4">Y2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a>  holds <br/><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> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font>, <font color="Maroon" title="c4">Y1</font>, <font color="Maroon" title="c5">Y2</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c4">Y1</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  &amp; <font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  &amp; <font color="Maroon" title="c4">Y1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) &amp; <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a>  implies <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
( <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c4">Y1</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  &amp; <font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">Y1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) or  not <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a>  or <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:41"/>
<font color="Maroon" title="c4">Y1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a>  or <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  )</span><br/>

<a NAME="E3:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c3">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="tsep_2.html#T32" target="_self" title="TSEP_2:th.32">Th34</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:41"/>
<font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> </span><br/>

<span class="kw">hence </span><a NAME="E5:41"/>
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E3:41"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="tsep_2.html#T39" target="_self" title="TSEP_2:th.39">Th41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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