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<b>let </b><font color="Maroon">NORM1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font>, <a href="numbers.html#K1">REAL</a> , <font color="Maroon">NORM2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font>, <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">NORM1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K2">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rsspace.html#K2">seq_id</a> <font color="Olive">x</font></span>)</span> <a href="lp_space.html#K1" target="_self">rto_power</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">p</font></span>)</span>
 <b>and </b><br/><a NAME="E2:13_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">NORM2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K2">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rsspace.html#K2">seq_id</a> <font color="Olive">x</font></span>)</span> <a href="lp_space.html#K1" target="_self">rto_power</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">p</font></span>)</span>
 ;<br/>

<a NAME="E3:13_1_1"/><i><font color="Green">E35</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">NORM1</font> <a href="hidden.html#R1">=</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">NORM2</font> <a href="hidden.html#R1">=</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:13_1_1"/>
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">z</font> <a href="hidden.html#R2">in</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">NORM1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">NORM2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:13_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E2:13_1_1_1"/>
<font color="Maroon">NORM1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K2">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rsspace.html#K2">seq_id</a> <font color="Maroon">z</font></span>)</span> <a href="lp_space.html#K1" target="_self">rto_power</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:13_1_1_1"/>
<font color="Maroon">NORM1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">NORM2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">z</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:13_1_1"/>
<font color="Maroon">NORM1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">NORM2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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