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<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> is <a href="jordan2c.html#V1">Bounded</a> )
 ;<br/>

<a NAME="E2:12"/>
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K10">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13">proj1</a>  <a href="pscomp_1.html#K12">||</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D30">PSCOMP_1:def 30</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">X</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i>, </i>;<br/>

<a NAME="E4:12"/>
 <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K11">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13">proj1</a>  <a href="pscomp_1.html#K12">||</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D32">PSCOMP_1:def 32</a></i>;<br/>
<b>hence </b><a NAME="E5:12"/>
 <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">X</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i>, </i>;<br/>

<a NAME="E6:12"/>
 <a href="pscomp_1.html#K18">S-bound</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K10">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="pscomp_1.html#K12">||</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D33">PSCOMP_1:def 33</a></i>;<br/>
<b>hence </b><a NAME="E7:12"/>
 <a href="pscomp_1.html#K18">S-bound</a> <font color="Maroon">X</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i>, </i>;<br/>

<a NAME="E8:12"/>
 <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K11">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="pscomp_1.html#K12">||</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D31">PSCOMP_1:def 31</a></i>;<br/>
<b>hence </b><a NAME="E9:12"/>
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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