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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">X1</font>,<font color="Olive" title="b2">X2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font> be   <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</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="Red">::  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#R4" title="TSEP_1:pred.4">are_weakly_separated</a> </span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c5">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X2</font> implies <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="tsep_1.html#R2" title="TSEP_1:pred.2">are_weakly_separated</a>  )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c6">B1</font> = <font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c7">B2</font> = <font color="Maroon" title="c5">A2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> ;<br/><span class="kw">assume </span><a NAME="E2:106_1"/>
( <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="tsep_1.html#R2" title="TSEP_1:pred.2">are_weakly_separated</a> </span><br/><a NAME="E3:106_1"/><span class="kw">then </span>
( <font color="Maroon" title="c6">B1</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c7">B2</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T16" target="_self" title="TSEP_1:th.16">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E4:106_1"/>
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="tsep_1.html#R2" title="TSEP_1:pred.2">are_weakly_separated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T54" target="_self" title="TSEP_1:th.54">Th54</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:106"/>
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R4" title="TSEP_1:pred.4">are_weakly_separated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#D9" target="_self" title="TSEP_1:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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