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<b>let </b><font color="Maroon">RNS</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">RNS</font>;<br/>



<span class="p1"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">x</font></span>)</span></span><a href="normsp_1.html#K1" target="_self">.||</a></span> = 
<span class="p1"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">RNS</font>)</span><a href="normsp_1.html#K1" target="_self">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
0
<b>by </b><i/>
;<br/>
<a NAME="E2:12"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">x</font></span><a href="normsp_1.html#K1" target="_self">.||</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">x</font></span><a href="normsp_1.html#K1" target="_self">.||</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:12"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">x</font></span><a href="normsp_1.html#K1" target="_self">.||</a></span> <a href="real_1.html#K3">+</a> <span class="p2"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">x</font></span><a href="normsp_1.html#K1" target="_self">.||</a></span></span>)</span> <a href="real_1.html#K6">/</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T138">XREAL_1:138</a></i>;<br/>
<b>hence </b><a NAME="E4:12"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1" target="_self">||.</a><span class="default"><font color="Maroon">x</font></span><a href="normsp_1.html#K1" target="_self">.||</a></span>
 ;<br/>


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