<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="rsspace4.html#V1" target="_self">bounded</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>;<br/>





<a NAME="E1:36"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="rsspace4.html#K4" target="_self">BoundedFunctions</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as    <a href="hidden.html#M1">set</a>  ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="rsspace4.html#K8" target="_self">BoundedFunctionsNorm</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">f</font> = 
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="rsspace4.html#K7" target="_self">PreNorms</a> <span class="p2">(<span class="default"><a href="rsspace4.html#K6" target="_self">modetrans</a> <font color="Maroon">f'</font>,<font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="rsspace4.html#K7" target="_self">PreNorms</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="txt" href="rsspace4.html#E1"><i><font color="Green">Lemma24</font></i></a></i>
;<br/>


</div>
