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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> non <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</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">X1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>  ex <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#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</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="b2">X2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> </span><br/><b>let </b><font color="Maroon" title="c2">X1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</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">  ex <font color="Olive" title="b1">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</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="Maroon" title="c2">X1</font>,<font color="Olive" title="b1">X2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> </span><br/>



<b>consider </b><font color="Maroon" title="c3">X2</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E2:67"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> 
 <b>by </b><i><a class="ref" href="tex_3.html#T8" target="_self" title="TEX_3:th.8">Th8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">X2</font> = <font color="Maroon" title="c3">X2</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E2:67"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="tex_3.html#T31" target="_self" title="TEX_3:th.31">Th31</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">X2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> </span><br/>

<b>thus </b><a NAME="E4:67"/>
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c4">X2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> 
 <b>by </b><i><a class="txt" href="#E2:67"><i><font color="Green" title="E27">A1</font></i></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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