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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="clopban1.html#V3" title="CLOPBAN1:attr.3">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="c1">X</font> holds  <font color="Olive" title="b1">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Olive" title="b3">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</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="clopban1.html#V3" title="CLOPBAN1:attr.3">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="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#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> = 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban2.html#T4" target="_self" title="CLOPBAN2:th.4">Th4</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="clopban2.html#T4" target="_self" title="CLOPBAN2:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="ref" href="clopban2.html#T4" target="_self" title="CLOPBAN2:th.4">Th4</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><b>end;</b></div>
<b>hence </b><a NAME="E2:11"/>
<font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="clopban2.html#K1" title="CLOPBAN2:func.1">*</a> <font color="Maroon" title="c4">h</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</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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