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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</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>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="clopban1.html#K8" title="CLOPBAN1:func.8">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Olive" title="b3">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Olive" title="b3">h</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font>, <font color="Maroon" title="c4">h</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="clopban1.html#K8" title="CLOPBAN1:func.8">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font></span><br/>



<a NAME="E1:13"/>
 <a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font></span>)</span>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="clopban1.html#D10" title="CLOPBAN1:def.10">CLOPBAN1:def 10</a></i>;<br/>
<a NAME="E2:13"/><b>then </b>
<span class="p1">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font></span>)</span>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p2">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="clopban2.html#T5" target="_self" title="CLOPBAN2:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
<font color="Maroon" title="c2">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K3" title="CLOPBAN2:func.3">*</a> <font color="Maroon" title="c4">h</font>
 <b>by </b><i><a class="ref" href="clopban1.html#D10" title="CLOPBAN1:def.10">CLOPBAN1:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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