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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="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V3">V7</a>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E14</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>3</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>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:13"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_2.html#E2:13"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E5:13"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
;<br/>
<a NAME="E6:13"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="normsp_1.html#T17">NORMSP_1:17</a></i>;<br/>
<a NAME="E7:13"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E4:13"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E8:13"/>
 <a href="bhsp_2.html#K1" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_2.html#E1:13"><i><font color="Green">E13</font></i></a>, <a class="ref" href="bhsp_2.html#T10" target="_self">Th10</a></i>;<br/>


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