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

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">bounded</a> <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds  <span class="p1">(<span class="default"><a href="lopban_1.html#K15" title="LOPBAN_1:func.15">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K14" title="LOPBAN_1:func.14">PreNorms</a> <font color="Olive" title="b1">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be  <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">bounded</a> <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="lopban_1.html#K15" title="LOPBAN_1:func.15">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K14" title="LOPBAN_1:func.14">PreNorms</a> <font color="Maroon" title="c3">f</font></span>)</span></span><br/>



<a NAME="E1:61"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D10" target="_self" title="LOPBAN_1:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c3">f</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="lopban_1.html#K15" title="LOPBAN_1:func.15">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">f</font> = 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K14" title="LOPBAN_1:func.14">PreNorms</a> <span class="p2">(<span class="default"><a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <font color="Maroon" title="c4">f'</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="lopban_1.html#E1:61"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="lopban_1.html#D14" target="_self" title="LOPBAN_1:def.14">Def14</a></i>
<br/>.= 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K14" title="LOPBAN_1:func.14">PreNorms</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="ref" href="lopban_1.html#T35" target="_self" title="LOPBAN_1:th.35">Th35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
