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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">Y0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon">A</font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 ;<br/><a NAME="E2:38_1"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y0</font> &amp; <font color="Olive">y</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y0</font> &amp; <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> &amp; ( for <font color="Olive">E</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>  holds <br/>(  not <font color="Olive">E</font> is <a href="pre_topc.html#V4">closed</a> or  not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">E</font> or <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">E</font> ) ) holds <br/> ex <font color="Olive">F</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">F</font> is <a href="pre_topc.html#V4">closed</a> &amp; not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> )
 <b>by </b><i>, <a class="ref" href="tsp_1.html#D1" target="_self">Def1</a></i>;<br/><b>hence </b><a NAME="E3:38_1"/>
<font color="Maroon">Y0</font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_2"/>
<font color="Maroon">Y0</font> is <a href="t_0topsp.html#V2">T_0</a>
 ;<br/><a NAME="E2:38_2"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> &amp; ( for <font color="Olive">E</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>  holds <br/>(  not <font color="Olive">E</font> is <a href="pre_topc.html#V4">closed</a> or  not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">E</font> or <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">E</font> ) ) holds <br/> ex <font color="Olive">F</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">F</font> is <a href="pre_topc.html#V4">closed</a> &amp; not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:38_2"/>
<font color="Maroon">A</font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 <b>by </b><i><a class="ref" href="tsp_1.html#D1" target="_self">Def1</a></i>;<br/></div>
<b>end;</b></div>


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