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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">V7</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:2"/><i><font color="Green">E3</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="normsp_1.html#D4">NORMSP_1:def 4</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bhsp_2.html#D1" target="_self">BHSP_2:def 1</a><br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E4:2"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>take </b><font color="Maroon">c<sub>6</sub></font> = 0;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E5:2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

 <a href="bhsp_1.html#K5">dist</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="bhsp_1.html#K5">dist</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="bhsp_2.html#E3:2"><i><font color="Green">E3</font></i></a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="bhsp_1.html#T41">BHSP_1:41</a></i>
;<br/>
<b>hence </b><a NAME="E7:2"/>
 <a href="bhsp_1.html#K5">dist</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_2.html#E4:2"><i><font color="Green">E4</font></i></a></i>;<br/>


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