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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="clopban1.html#V2" title="CLOPBAN1:attr.2">bounded</a>  <a href="clopban1.html#NM1" title="CLOPBAN1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds   <a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="clopban1.html#V2" title="CLOPBAN1:attr.2">bounded</a>  <a href="clopban1.html#NM1" title="CLOPBAN1: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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font></span><br/>



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<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="clopban1.html#K8" title="CLOPBAN1:func.8">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="clopban1.html#D8" target="_self" title="CLOPBAN1:def.8">Def8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:59"/>
 <a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="clopban1.html#D10" target="_self" title="CLOPBAN1:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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