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<b>set </b><font color="Maroon">lp</font> =  <a href="normsp_1.html#G1">NORMSTR</a>(# <span class="p1">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K10">Zero_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K8">Add_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K9">Mult_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="lp_space.html#K3" target="_self">l_norm^</a> <font color="Maroon">p</font></span>)</span> #);<br/>
<b>reconsider </b><font color="Maroon">lp</font> =  <a href="normsp_1.html#G1">NORMSTR</a>(# <span class="p1">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K10">Zero_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K8">Add_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K9">Mult_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="lp_space.html#K3" target="_self">l_norm^</a> <font color="Maroon">p</font></span>)</span> #) as   <a href="normsp_1.html#NM1">RealNormSpace</a> <b>by </b><i>, <a class="ref" href="lp_space.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E2:29_1_1"/>
for <font color="Olive">vseq</font> being  <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">lp</font>  st <font color="Olive">vseq</font> is <a href="rsspace3.html#V1">CCauchy</a> holds <br/><font color="Olive">vseq</font> is <a href="normsp_1.html#V4">convergent</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:29_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">lp</font> is <a href="lopban_1.html#V4">complete</a>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D16">LOPBAN_1:def 16</a></i>;<br/>
<b>thus </b><a NAME="E4:29_1_1"/>
 <a href="normsp_1.html#G1">NORMSTR</a>(# <span class="p1">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K10">Zero_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K8">Add_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K9">Mult_</a> <span class="p2">(<span class="default"><a href="lp_space.html#K2" target="_self">the_set_of_RealSequences_l^</a> <font color="Maroon">p</font></span>)</span>,<a href="rsspace.html#K7">Linear_Space_of_RealSequences</a> </span>)</span>,<span class="p1">(<span class="default"><a href="lp_space.html#K3" target="_self">l_norm^</a> <font color="Maroon">p</font></span>)</span> #) is   <a href="lopban_1.html#NM2">RealBanachSpace</a>
 <b>by </b><i/>;<br/>


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